28215: An Interesting Number

I've heard it said that all numbers are interesting and that, if a number is not, then it's interesting because it's not. The number associated with my diurnal age today (\( \textbf{28215}\) ) is definitely interesting. 

FIRST INTERESTING PROPERTY

Its prime factorisation is as follows:$$28215=3^3 \times 5 \times 11 \times 19$$It has 32 proper divisors and these are:

1, 3, 5, 9, 11, 15, 19, 27, 33, 45, 55, 57, 95, 99, 135, 165, 171, 209, 285, 297, 495, 513, 627, 855, 1045, 1485, 1881, 2565, 3135, 5643, 9405

The sum of these divisors is 29385 and so the number is abundant because this sum exceeds the number itself. Furthermore, all of these divisors are deficient and this makes it primitive abundant. Lastly the number is odd. This makes 28215 an odd primitive abundant number and these sorts of numbers are quite rare. Here is the list of the 50 such numbers up to 40000 (permalink):

945, 1575, 2205, 3465, 4095, 5355, 5775, 5985, 6435, 6825, 7245, 7425, 8085, 8415, 8925, 9135, 9555, 9765, 11655, 12705, 12915, 13545, 14805, 15015, 16695, 18585, 19215, 19635, 21105, 21945, 22365, 22995, 23205, 24885, 25935, 26145, 26565, 28035, \( \textbf{28215}\), 29835, 30555, 31395, 31815, 32445, 33345, 33495, 33915, 34155, 35805, 39585

SECOND INTERESTING PROPERTY

It can be seen from its factorisation that 28215 is 6-almost prime and its reversal, 51282, is also 6-almost prime:$$ \begin{align} 28215 &=3^3 \times 5 \times 11 \times 19 \\ 51282 &= 2 \times 3^2 \times 7 \times 11 \times 37 \end{align}$$While this property is not quite are rare as being odd primitive abundant, there are still only 118 such numbers in the range up to 40000. These are (permalink):

2576, 2772, 2970, 2992, 4284, 4356, 4410, 4600, 4698, 4824, 5265, 5625, 6534, 6752, 6776, 6900, 8008, 8250, 8964, 10710, 10890, 13140, 13986, 16236, 16335, 17577, 18504, 19494, 20286, 20574, 21112, 21114, 21150, 21160, 21336, 21492, 21576, 21609, 21712, 21900, 21912, 21996, 22392, 22770, 22788, 22824, 22869, 23058, 23247, 23250, 23496, 23562, 23580, 23598, 23632, 23832, 24156, 24660, 24975, 25020, 25092, 25104, 25164, 25245, 25300, 25416, 25434, 25452, 25608, 25668, 25752, 25952, 26163, 26334, 26532, 27060, 27108, 27135, 27192, 27240, 27248, 27270, 27405, 27408, 27468, 27472, 27588, 27608, 27636, 27816, 28116, \( \textbf{28215} \), 28314, 28710, 28782, 28890, 29052, 29172, 29322, 29340, 29392, 29412, 29580, 29750, 29784, 29835, 29900, 29960, 29984, 32967, 34965, 35775, 35937, 36162, 36990, 37026, 38367, 38934

I explore this reversibility extensively in my post titled Beyond Emirp from July 2025.

THIRD INTERESTING PROPERTY

The totient of a number \(n\) (commonly known as Euler's totient function or phi function, denoted as \(\phi(n)\)) counts the number of positive integers up to \(n\) that share no common factors with \(n\) other than 1. These numbers are called "relatively prime" or "coprime" to \(n\).

28215 has the property that it and its reversal, 51282, both have the same totient. Thus:$$ \phi(28215)=\phi(51282)=12960 $$This property is the rarest of all because in the range up to 40000 there are only 25 numbers with this property. They are:

190, 427, 429, 724, 924, 4147, 4697, 6276, 6726, 7414, 7964, 9079, 9709, 10040, 10940, 14450, 15860, 19190, 20493, 20553, 28092, \( \textbf{28215}\), 29082, 35502, 39402

FOURTH INTERESTING PROPERTY

28215 is a member of OEIS  A076773:

A076773   2-nadirs of \( \phi\) : numbers \( k \text{ such that }\)  

\( \phi(k-2) \gt \phi(k-1) \gt \phi(k) \lt \phi(k+1) \lt \phi(k+2) \)

I covered this in a post titled Totient Function: Jagged Versus Rounded Local Minima back in March of 2025. Figure 1 gives an idea of what is going on:

Figure 1

Here the \(\phi\) values for 28213, 28214, 26215, 28216, 28217 are:$$27808 \lt14106 \lt 12960 \lt14104 \lt23184$$There are 238 such minima in the range up to 40000:

315, 525, 735, 1155, 1365, 1575, 1755, 1785, 1815, 1995, 2145, 2415, 2475, 2805, 3045, 3315, 3465, 3885, 4095, 4125, 4305, 4515, 4725, 4935, 5115, 5145, 5355, 5775, 6045, 6195, 6405, 6435, 6615, 6825, 7035, 7095, 7245, 7395, 7455, 7605, 7665, 8085, 8265, 8505, 8715, 8745, 8925, 9135, 9345, 9405, 9555, 9735, 9765, 9975, 10185, 10395, 10455, 10545, 10815, 10965, 11055, 11235, 11385, 11445, 11655, 11865, 12075, 12285, 12495, 12675, 12705, 12915, 13125, 13335, 13545, 13695, 13965, 14025, 14175, 14355, 14385, 14595, 14805, 14835, 15015, 15045, 15225, 15405, 15435, 15645, 15675, 15855, 16005, 16065, 16275, 16335, 16485, 16695, 16905, 17085, 17325, 17355, 17745, 17955, 18135, 18165, 18375, 18585, 18645, 18795, 18975, 19215, 19425, 19635, 19665, 20055, 20265, 20295, 20475, 20625, 20685, 20865, 20895, 21105, 21255, 21315, 21525, 21945, 22365, 22425, 22575, 22605, 22785, 22995, 23205, 23265, 23415, 23595, 23625, 23655, 23835, 23985, 24225, 24255, 24675, 24885, 24915, 25095, 25245, 25305, 25515, 25575, 25725, 25905, 25935, 26145, 26325, 26565, 26775, 26985, 27027, 27195, 27615, 27825, 27885, 28035, \( \textbf{28215}\), 28245, 28275, 28455, 28665, 28815, 28875, 29055, 29295, 29505, 29865, 29925, 30195, 30345, 30555, 30723, 30765, 30975, 31185, 31365, 31395, 31605, 31815, 32025, 32175, 32235, 32445, 32655, 32835, 32895, 33033, 33075, 33345, 33495, 33705, 33735, 33915, 34125, 34155, 34335, 34485, 34515, 34545, 34755, 34965, 35175, 35385, 35805, 36225, 36435, 36465, 36645, 36795, 36855, 37065, 37275, 37455, 37485, 37695, 37905, 38115, 38535, 38745, 38775, 38955, 39165, 39195, 39375, 39435, 39585, 39765, 39795

FIFTH INTERESTING PROPERTY

28215 is also a member of A323380:

A323380  2-zeniths of \(\sigma\): numbers \( k \text{ such that }\)

                    \( \sigma(k-2) \lt \sigma(k-1) \lt \sigma(k) \gt \sigma(k+1) \gt \sigma(k+2) \)

I covered this in a post titled Totient and Sigma Graphs Revisited in August of 2025. Figure 2 shows what's going on and it's the local zenith replacing the local nadir of the totient graph:

Figure 2

Here the sigma values for 28213, 28214, 26215, 28216, 28217 are:$$28620 \lt 42324 \lt 57600 \gt52920 \gt 33600$$Below is a list of numbers up to 40000 that belong to BOTH OEIS A323380 and OEIS A076773 (sigma and totient respectively):

315, 525, 1155, 1575, 1755, 1785, 1995, 2475, 2805, 3045, 3315, 3465, 3885, 4095, 4125, 4515, 4725, 5115, 5355, 5775, 6045, 6195, 6405, 6435, 6615, 6825, 7035, 7245, 7605, 8085, 8505, 8715, 8925, 9135, 9405, 9555, 9765, 9975, 10395, 11235, 11385, 11445, 11655, 12075, 12285, 12675, 12705, 12915, 13125, 13545, 13965, 14025, 14175, 14355, 14595, 14805, 15015, 15435, 15645, 15675, 16005, 16065, 16275, 16335, 16695, 16905, 17325, 17745, 17955, 18135, 18375, 18585, 18795, 19215, 19635, 20475, 20685, 21105, 21315, 21525, 21945, 22365, 22605, 22995, 23205, 23595, 23625, 23835, 24255, 24675, 24885, 24915, 25245, 25515, 25725, 25935, 26325, 26565, 26775, 27027, 27195, 27885, 28035, \( \textbf{28215}\), 28245, 28275, 28665, 28875, 29295, 29925, 30195, 30345, 30555, 30723, 30765, 31185, 31365, 31395, 31605, 31815, 32025, 32175, 32235, 32445, 32835, 33075, 33345, 33495, 33915, 34125, 34155, 34485, 34515, 34755, 34965, 35175, 35805, 36225, 36435, 36645, 36795, 36855, 37275, 37485, 38115, 38745, 38955, 39165, 39195, 39375, 39435, 39585, 39765, 39795

SIXTH INTERESTING PROPERTY

28215 has a totient and sum of divisors that have 2, 3 and 5 as their distinct prime factors:$$ \begin{align} \sigma(28215) &= 57600 = 2^8 \times 3^2 \times 5^2 \rightarrow 2, 3, 5 \text{ as distinct prime factors} \\ \phi(28215) &= 12960 = 2^5 \times 3^4 \times 5 \rightarrow 2, 3, 5 \text{ as distinct prime factors} \end{align} $$There are 143 such numbers in the range from 28215 to 40000:

\( \textbf{28215} \), 28258, 28329, 28340, 28424, 28458, 28614, 28728, 28768, 28782, 28809, 28826, 28985, 29029, 29222, 29260, 29295, 29337, 29393, 29512, 29640, 29667, 29678, 29835, 29848, 30039, 30184, 30240, 30264, 30305, 30381, 30504, 30566, 30760, 30780, 30814, 30888, 30914, 30943, 30956, 30996, 31008, 31027, 31160, 31174, 31283, 31331, 31392, 31416, 31465, 31496, 31529, 31806, 31816, 32103, 32130, 32131, 32298, 32376, 32395, 32589, 32604, 32718, 32802, 32984, 33015, 33176, 33292, 33345, 33383, 33440, 33480, 33495, 33497, 33528, 33572, 33592, 33836, 33885, 33915, 34008, 34162, 34276, 34293, 34317, 34440, 34452, 34573, 34580, 34605, 34782, 34884, 35061, 35074, 35112, 35340, 35343, 35424, 35464, 35530, 35752, 35805, 35910, 35948, 35960, 36366, 36423, 36666, 36828, 36859, 36860, 36890, 36920, 37060, 37128, 37417, 37638, 37719, 37730, 37758, 37772, 37961, 38038, 38152, 38285, 38340, 38368, 38408, 38610, 38745, 38760, 38874, 39032, 39121, 39219, 39270, 39370, 39458, 39501, 39520, 39556, 39576, 39729

SEVENTH INTERESTING PROPERTY

28215 is what I've termed an \(a,b,c,d\) number because it can be combined with three other numbers, all with the same digits, to form a simple additive equation and this can be done in two different ways. Here is what I mean:$$ \begin{align} 25182 + 28125 + \textbf{28215} &= 81522 \\ 25812 + 28125 + \textbf{28215} &= 82152 \end{align}$$Here are the numbers with this property in the range from 28215 to 40000:

\( \textbf{28215}\), 28260, 28269, 28359, 28413, 28458, 28467, 28476, 28512, 28521, 28539, 28548, 28593, 28611, 28647, 28674, 28692, 28701, 28710, 28719, 28746, 28764, 28791, 28845, 28854, 28863, 28917, 28935, 28953, 28962, 28971, 29016, 29034, 29043, 29061, 29106, 29160, 29178, 29187, 29268, 29304, 29340, 29358, 29367, 29385, 29394, 29439, 29448, 29475, 29493, 29538, 29583, 29601, 29610, 29628, 29637, 29673, 29682, 29718, 29754, 29763, 29781, 29817, 29835, 29853, 29871, 29961, 30015, 30150, 30159, 30168, 30195, 30285, 30294, 30429, 30492, 30519, 30582, 30591, 30627, 30681, 30726, 30825, 30852, 30924, 30942, 30951, 31059, 31068, 31149, 31158, 31176, 31185, 31464, 31491, 31509, 31590, 31599, 31608, 31635, 31644, 31653, 31680, 31689, 31698, 31761, 31788, 31806, 31815, 31842, 31860, 31869, 31878, 31896, 31905, 31959, 31968, 31986, 31995, 32049, 32076, 32085, 32148, 32418, 32481, 32490, 32499, 32580, 32607, 32679, 32697, 32760, 32769, 32796, 32814, 32841, 32850, 32859, 32886, 32895, 32904, 32958, 32967, 32976, 32985, 32994, 34029, 34119, 34128, 34164, 34182, 34218, 34281, 34299, 34461, 34614, 34641, 34812, 34821, 34911, 34992, 35019, 35082, 35091, 35109, 35118, 35190, 35217, 35271, 35631, 35712, 35721, 35802, 35820, 35829, 35892, 35910, 35982, 35991, 36018, 36108, 36117, 36135, 36144, 36153, 36171, 36198, 36261, 36279, 36288, 36297, 36315, 36351, 36414, 36513, 36531, 36621, 36711, 36729, 36792, 36810, 36819, 36918, 36927, 36972, 36981, 37116, 37125, 37161, 37179, 37197, 37215, 37251, 37269, 37296, 37521, 37611, 37629, 37719, 37917, 37962, 38016, 38061, 38106, 38115, 38142, 38151, 38160, 38169, 38187, 38196, 38214, 38241, 38286, 38295, 38412, 38511, 38529, 38592, 38610, 38619, 38682, 38691, 38817, 38826, 38871, 38916, 38925, 38952, 38961, 39015, 39024, 39042, 39051, 39105, 39150, 39159, 39177, 39186, 39195, 39204, 39258, 39285, 39402, 39411, 39420, 39492, 39501, 39510, 39528, 39582, 39591, 39618, 39627, 39672, 39681, 39717, 39726, 39762, 39816, 39825, 39852, 39861, 39942, 39951

EIGHTH INTERESTING PROPERTY

If the prime factors, with multiplicity, of 28215 are concatenated in ascending order, they form a prime number. Thus:$$28215 =3^3 \times 5 \times 11 \times 19 \rightarrow 33351119$$Such a prime is called the home prime and so 28215 is only one step removed from its home prime. There are many other concatenations that yield primes and all the possibilities are listed below (permalink):

11193353, 11319533, 11335193, 19331153, 19335311, 19351133, 19511333, 31119353, 31131953, 31133519, 31153193, 31933511, 31951133, 31953113, 33191153, 33195311, 33311519, \( \textbf{33351119} \), 35113193, 35191133, 35193311, 35319113, 35331119, 35331911, 51131933, 51133193

This property, of being one step removed from its home prime, is relatively common but nonetheless interesting.

NINTH INTERESTING PROPERTY

28215 is a member of the commas sequence beginning with 8. I explore sequences of this type in my blog post The Commas Sequence from December of 2023. The full trajectory up to 40000 is as follows:

[8, 97, 168, 250, 252, 274, 317, 390, 393, 427, 502, 527, 603, 639, 736, 804, 852, 880, 888, 977, 1048, 1129, 1220, 1221, 1232, 1253, 1284, 1325, 1376, 1437, 1508, 1589, 1680, 1681, 1692, 1713, 1744, 1785, 1836, 1897, 1968, 2050, 2052, 2074, 2116, 2178, 2260, 2262, 2284, 2326, 2388, 2470, 2472, 2494, 2536, 2598, 2680, 2682, 2704, 2746, 2808, 2890, 2892, 2914, 2956, 3019, 3112, 3135, 3188, 3271, 3284, 3327, 3400, 3403, 3436, 3499, 3592, 3615, 3668, 3751, 3764, 3807, 3880, 3883, 3916, 3979, 4073, 4107, 4181, 4195, 4249, 4343, 4377, 4451, 4465, 4519, 4613, 4647, 4721, 4735, 4789, 4883, 4917, 4991, 5006, 5071, 5086, 5151, 5166, 5231, 5246, 5311, 5326, 5391, 5406, 5471, 5486, 5551, 5566, 5631, 5646, 5711, 5726, 5791, 5806, 5871, 5886, 5951, 5966, 6032, 6058, 6144, 6190, 6196, 6262, 6288, 6374, 6420, 6426, 6492, 6518, 6604, 6650, 6656, 6722, 6748, 6834, 6880, 6886, 6952, 6978, 7065, 7122, 7149, 7246, 7313, 7350, 7357, 7434, 7481, 7498, 7585, 7642, 7669, 7766, 7833, 7870, 7877, 7954, 8002, 8030, 8038, 8126, 8194, 8242, 8270, 8278, 8366, 8434, 8482, 8510, 8518, 8606, 8674, 8722, 8750, 8758, 8846, 8914, 8962, 8990, 8998, 9087, 9166, 9235, 9294, 9343, 9382, 9411, 9430, 9439, 9538, 9627, 9706, 9775, 9834, 9883, 9922, 9951, 9970, 9979, 10070, 10071, 10082, 10103, 10134, 10175, 10226, 10287, 10358, 10439, 10530, 10531, 10542, 10563, 10594, 10635, 10686, 10747, 10818, 10899, 10990, 10991, 11002, 11023, 11054, 11095, 11146, 11207, 11278, 11359, 11450, 11451, 11462, 11483, 11514, 11555, 11606, 11667, 11738, 11819, 11910, 11911, 11922, 11943, 11974, 12015, 12066, 12127, 12198, 12279, 12370, 12371, 12382, 12403, 12434, 12475, 12526, 12587, 12658, 12739, 12830, 12831, 12842, 12863, 12894, 12935, 12986, 13047, 13118, 13199, 13290, 13291, 13302, 13323, 13354, 13395, 13446, 13507, 13578, 13659, 13750, 13751, 13762, 13783, 13814, 13855, 13906, 13967, 14038, 14119, 14210, 14211, 14222, 14243, 14274, 14315, 14366, 14427, 14498, 14579, 14670, 14671, 14682, 14703, 14734, 14775, 14826, 14887, 14958, 15039, 15130, 15131, 15142, 15163, 15194, 15235, 15286, 15347, 15418, 15499, 15590, 15591, 15602, 15623, 15654, 15695, 15746, 15807, 15878, 15959, 16050, 16051, 16062, 16083, 16114, 16155, 16206, 16267, 16338, 16419, 16510, 16511, 16522, 16543, 16574, 16615, 16666, 16727, 16798, 16879, 16970, 16971, 16982, 17003, 17034, 17075, 17126, 17187, 17258, 17339, 17430, 17431, 17442, 17463, 17494, 17535, 17586, 17647, 17718, 17799, 17890, 17891, 17902, 17923, 17954, 17995, 18046, 18107, 18178, 18259, 18350, 18351, 18362, 18383, 18414, 18455, 18506, 18567, 18638, 18719, 18810, 18811, 18822, 18843, 18874, 18915, 18966, 19027, 19098, 19179, 19270, 19271, 19282, 19303, 19334, 19375, 19426, 19487, 19558, 19639, 19730, 19731, 19742, 19763, 19794, 19835, 19886, 19947, 20019, 20111, 20123, 20155, 20207, 20279, 20371, 20383, 20415, 20467, 20539, 20631, 20643, 20675, 20727, 20799, 20891, 20903, 20935, 20987, 21059, 21151, 21163, 21195, 21247, 21319, 21411, 21423, 21455, 21507, 21579, 21671, 21683, 21715, 21767, 21839, 21931, 21943, 21975, 22027, 22099, 22191, 22203, 22235, 22287, 22359, 22451, 22463, 22495, 22547, 22619, 22711, 22723, 22755, 22807, 22879, 22971, 22983, 23015, 23067, 23139, 23231, 23243, 23275, 23327, 23399, 23491, 23503, 23535, 23587, 23659, 23751, 23763, 23795, 23847, 23919, 24011, 24023, 24055, 24107, 24179, 24271, 24283, 24315, 24367, 24439, 24531, 24543, 24575, 24627, 24699, 24791, 24803, 24835, 24887, 24959, 25051, 25063, 25095, 25147, 25219, 25311, 25323, 25355, 25407, 25479, 25571, 25583, 25615, 25667, 25739, 25831, 25843, 25875, 25927, 25999, 26091, 26103, 26135, 26187, 26259, 26351, 26363, 26395, 26447, 26519, 26611, 26623, 26655, 26707, 26779, 26871, 26883, 26915, 26967, 27039, 27131, 27143, 27175, 27227, 27299, 27391, 27403, 27435, 27487, 27559, 27651, 27663, 27695, 27747, 27819, 27911, 27923, 27955, 28007, 28079, 28171, 28183, \( \textbf{28215} \), 28267, 28339, 28431, 28443, 28475, 28527, 28599, 28691, 28703, 28735, 28787, 28859, 28951, 28963, 28995, 29047, 29119, 29211, 29223, 29255, 29307, 29379, 29471, 29483, 29515, 29567, 29639, 29731, 29743, 29775, 29827, 29899, 29991, 30004, 30047, 30120, 30123, 30156, 30219, 30312, 30335, 30388, 30471, 30484, 30527, 30600, 30603, 30636, 30699, 30792, 30815, 30868, 30951, 30964, 31007, 31080, 31083, 31116, 31179, 31272, 31295, 31348, 31431, 31444, 31487, 31560, 31563, 31596, 31659, 31752, 31775, 31828, 31911, 31924, 31967, 32040, 32043, 32076, 32139, 32232, 32255, 32308, 32391, 32404, 32447, 32520, 32523, 32556, 32619, 32712, 32735, 32788, 32871, 32884, 32927, 33000, 33003, 33036, 33099, 33192, 33215, 33268, 33351, 33364, 33407, 33480, 33483, 33516, 33579, 33672, 33695, 33748, 33831, 33844, 33887, 33960, 33963, 33996, 34059, 34152, 34175, 34228, 34311, 34324, 34367, 34440, 34443, 34476, 34539, 34632, 34655, 34708, 34791, 34804, 34847, 34920, 34923, 34956, 35019, 35112, 35135, 35188, 35271, 35284, 35327, 35400, 35403, 35436, 35499, 35592, 35615, 35668, 35751, 35764, 35807, 35880, 35883, 35916, 35979, 36072, 36095, 36148, 36231, 36244, 36287, 36360, 36363, 36396, 36459, 36552, 36575, 36628, 36711, 36724, 36767, 36840, 36843, 36876, 36939, 37032, 37055, 37108, 37191, 37204, 37247, 37320, 37323, 37356, 37419, 37512, 37535, 37588, 37671, 37684, 37727, 37800, 37803, 37836, 37899, 37992, 38015, 38068, 38151, 38164, 38207, 38280, 38283, 38316, 38379, 38472, 38495, 38548

So, overall, 28215 is a very interesting number.

Neglected Numbers

Sometimes it's easy to give up on numbers. Take 26271 for example. This number represents my diurnal age today and when I searched in the OEIS nothing of interest showed up. Even a search using OEIS + 26271, which often throws up OEIS b-files containing the number, didn't reveal anything interesting. 

Figure 1: link

In such situations I fall back on the Sequence Database: a database with 2402879 machine generated integer and decimal sequences. I discovered this site in June of 2020. Unfortunately, this didn't turn up any sequences of interest either but then I remembered another site that lists sequences (see Figure 1). 

It was here that I found something of substance. See Figure 2.

Figure 2

26271 belongs to a sequence of numbers \(n\) with the property that \(n\) is 5-almost prime and \(n+1 \) is 6-almost prime. In the case of 26271, it factors to \(3^3 \times 7 \times 139 \) and 26272 factors to \(2^5 \times 821\). The example of 728, the first member of the sequence, is given in Figure 1.

It's easy enough to generate this sequence in SageMath, using the algorithm shown in Figure 3:

Figure 3: permalink

This algorithm can be easily modified to search for other patterns involving \(k\)-almost primes where \(k \geq 2\). For example, what numbers \(n\) are there, up to 26271, with the property that \(n\) is 4-almost prime and \(n+1 \) is 5-almost prime? These numbers turn out to be quite numerous and I won't list them all here but notice how 26270 makes an appearance:

495, 975, 1071, 1287, 1484,  ... , 26075, 26103, 26195, 26215, 26270

From this we can see that 26271 is the middle term in a triplet of numbers with the property that: 

• \(26270 = 2 \times 5 \times 37 \times 71\) and is 4-almost prime
• \(26271 = 3^3 \times 7 \times 139 \) and is 5-almost prime
• \(26272 = 2^5 \times 821\) and is 6-almost prime

This condition could be a good candidate for admission to the OEIS. It could be framed as follows:

Numbers \(n\) such that \(n-1\) is 4-almost prime, \(n\) is 5-almost prime and \(n+1\) is 6-almost prime.

Up to 100,000 the members of this sequence are:

11151, 13455, 23375, 26271, 31311, 33776, 36125, 40375, 45495, 46375, 48411, 49049, 49167, 61335, 63125, 74151, 77895, 78111, 78351, 80271, 82575, 83511, 84591, 86031, 87375, 88749, 90207

I checked and this sequence is not currently in the OEIS so I'll put it forward as a candidate and report back here when it's approved.

Reporting back, I'm happy to report that the sequence was approved, although one of the arbiters took exception to my use of the term \(n\)-almost prime and suggested that it be replaced by composite with \(n\) prime factors. I followed this suggestion (always a good idea to keep the arbiters on side) and the result is OEIS A342246:

A342246

Numbers \(n\) such that \(n-1\), \(n\) and \(n+1\) are all composite with four, five and six (not necessarily distinct) prime factors respectively

Before I discovered the 5-almost prime and 6-almost prime link on the Italian site, I also made a discovery of my own. 26271 is a member of a sequence of numbers such that the sum of its digits is equal to the sum of the digits of its totient. Here the digits of 26271 add to 18 and the digits of its totient 14904 also add to 18. Up to 26271, about 7.61% of numbers have this property. The members of this sequence, up to 1000, are as follows:

1, 21, 27, 34, 54, 63, 81, 106, 108, 117, 126, 129, 135, 136, 142, 147, 156, 162, 171, 178, 195, 205, 212, 214, 216, 234, 237, 243, 252, 270, 272, 291, 315, 324, 333, 342, 351, 356, 358, 394, 402, 405, 424, 432, 441, 459, 493, 502, 504, 513, 538, 540, 544, 565, 585, 624, 630, 663, 702, 712, 714, 716, 718, 723, 729, 745, 804, 810, 831, 834, 835, 840, 864, 873, 918, 932, 934, 936, 943, 981

This discovery also prompted me to investigate the sum of the digits of the sum of the divisors. The percentage of numbers whose sum of digits equals the sum of the digits of the sum of its divisors is 4.59%. The members of this sequence, up to 1000, are as follows:

1, 15, 24, 64, 69, 78, 90, 114, 133, 147, 153, 186, 198, 258, 270, 276, 288, 306, 339, 360, 366, 393, 429, 474, 492, 495, 507, 522, 582, 588, 609, 618, 627, 639, 708, 717, 738, 762, 763, 801, 817, 834, 846, 871, 906, 933, 960, 978, 990

The percentage of numbers whose sum of digits equals both the sum of the digits of the sum of its divisors AND the sum of the digits of its totient is 0.727%. The members of this sequence, up to 10000, are as follows:

1, 147, 270, 834, 1158, 1374, 1377, 2028, 2214, 2436, 2454, 2538, 2592, 2646, 2754, 2862, 2907, 3339, 3726, 4293, 4320, 4371, 4614, 5049, 5262, 5319, 5472, 5508, 5607, 5670, 5751, 5802, 6234, 6291, 6426, 6570, 6972, 7155, 7209, 7434, 7560, 7605, 7614, 8190, 8934, 9126, 9270, 9315, 9333, 9342, 9720, 9744, 9810

This last sequence might be an interesting one for admission to the OEIS (as it's not currently in there) but I'll wait until my current submission is approved. This is again easy to generate in SageMath as Figure 4 shows:

Figure 4: permalink

In conclusion, it can be said that 26271 is an Ulam number, being the sum of two previous Ulam numbers, namely 47 and 26224. It is also a happy number since repeated sums of squares of digits lead to 1. However, as we've seen, it also has other interesting properties that a little research uncovered.