Sphenic Number Chains

My previous post on the topic of chains of semiprimes in arithmetic progression prompted me to investigate similar chains formed by sphenic numbers. This time we are looking for the smallest sphenic number that is at the end of an arithmetic progression of \(n\) sphenic numbers as \(n\) ranges from 1 upwards. The result for \(n\) up to 18 is as follows (permalink):

30, 42, 102, 138, 174, 442, 1010, 2278, 2422, 6494, 10322, 10586, 12694, 21434, 28466, 56426, 62902, 145930

Let's look at 28466 that is at the end of a chain of 15 sphenic numbers with a common difference of 96 (permalink):

Arithmetic Progression of 15 Sphenic Numbers

Common Difference: 96

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Term   | Sphenic Number   | Factorisation

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1      | 27122            | 2 x 71 x 191

2      | 27218            | 2 x 31 x 439

3      | 27314            | 2 x 7 x 1951

4      | 27410            | 2 x 5 x 2741

5      | 27506            | 2 x 17 x 809

6      | 27602            | 2 x 37 x 373

7      | 27698            | 2 x 11 x 1259

8      | 27794            | 2 x 13 x 1069

9      | 27890            | 2 x 5 x 2789

10     | 27986            | 2 x 7 x 1999

11     | 28082            | 2 x 19 x 739

12     | 28178            | 2 x 73 x 193

13     | 28274            | 2 x 67 x 211

14     | 28370            | 2 x 5 x 2837

15     | 28466            | 2 x 43 x 331

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Other tables can be generated for the other values of \(n\) but the above table is the most relevant because it covers numbers (28274, 28370 and 28466) that are upcoming for me in terms of my diurnal age.

Here are the results for 16 sphenic numbers in arithmetic progression:

Arithmetic Progression of 16 Sphenic Numbers

Common Difference: 708

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Term   | Sphenic Number   | Factorisation

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1      | 45806            | 2 x 37 x 619

2      | 46514            | 2 x 13 x 1789

3      | 47222            | 2 x 7 x 3373

4      | 47930            | 2 x 5 x 4793

5      | 48638            | 2 x 83 x 293

6      | 49346            | 2 x 11 x 2243

7      | 50054            | 2 x 29 x 863

8      | 50762            | 2 x 17 x 1493

9      | 51470            | 2 x 5 x 5147

10     | 52178            | 2 x 7 x 3727

11     | 52886            | 2 x 31 x 853

12     | 53594            | 2 x 127 x 211

13     | 54302            | 2 x 19 x 1429

14     | 55010            | 2 x 5 x 5501

15     | 55718            | 2 x 13 x 2143

16     | 56426            | 2 x 89 x 317

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