The number associated with my diurnal age today,
In developing my algorithm (permalink), I naturally only considered composite numbers but I also required the sum of divisors and the totient to be composite as well. It turns out that there are 785 such numbers with the smallest being 14:
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Table 1: permalink |
Here is the full list of the 146 numbers between 27838 and 40000 (permalink):
27838, 27956, 28126, 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
If we consider the sum of the
42, 78, 90, 93, 135, 198, 216, 219, 259, 270, 273, 360, 364, 403, 438, 679, 723, 738, 793, 988, 1080, 1299, 1333, 1446, 1683, 1722, 1793, 1818, 1924, 2009, 2044, 2263, 2295, 2623, 2743, 2754, 2970, 3135, 3157, 3162, 3258, 3420, 3589, 3796, 3960, 4284, 4320, 4440, 4453, 4564, 4905, 5187, 5824, 5983, 5995, 6893, 6918, 7320, 7373, 7380, 7392, 7783, 7980, 8928, 8987, 9504, 9720, 9943, 10864, 10920, 11023, 11538, 11653, 11904, 14233, 15613, 15813, 16764, 17593, 18019, 20202, 22625, 24199, 24339, 24613, 25275, 25324, 25792, 27133, 28243, 28564, 30240, 30303, 30623, 31408, 31992, 32283, 32284, 34300, 34393, 34933, 36421, 36720, 39283
Not all the prime factors of the sum of proper divisors begin with 2 as can be seen in Table 2 that shows the details for numbers between 28000 and 40000:
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Table 2: permalink |
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