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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A304000 Numbers whose sum of divisors is the eighth power of one of their divisors.

Original entry on oeis.org

1, 600270, 621690, 669990, 685290, 693294, 699810, 725934, 774894, 782598, 813378, 823938, 839802, 508541124, 553420812, 678160756, 127444892484, 130213538364, 131470441284, 131515433868, 131523414204, 131528229924, 137156770884, 139602234324, 140161757484
Offset: 1

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Author

Paolo P. Lava, May 04 2018

Keywords

Comments

Subset of A048258.
If m and n are coprime members of the sequence, then m*n is in the sequence. However, it is not clear whether there are such m and n where neither is 1: in particular, are there odd members other than 1? - Robert Israel, May 10 2018

Examples

			Divisors of 600270 are 1, 2, 3, 5, 6, 10, 11, 15, 17, 22, 30, 33, 34, 51, 55, 66, 85, 102, 107, 110, 165, 170, 187, 214, 255, 321, 330, 374, 510, 535, 561, 642, 935, 1070, 1122, 1177, 1605, 1819, 1870, 2354, 2805, 3210, 3531, 3638, 5457, 5610, 5885, 7062, 9095, 10914, 11770, 17655, 18190, 20009, 27285, 35310, 40018, 54570, 60027, 100045, 120054, 200090, 300135, 600270 and their sum is 1679616 = 6^8.

Crossrefs

Cf. A000203, A048258, A303123, A303993, A303994, A303995, A303996, A303999.

Programs

  • Maple
    with(numtheory): P:=proc(q) local a,k,n;
for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a) do if sigma(n)=a[k]^8 then print(n); break; fi; od; od; end: P(10^9);
  • PARI
    isok(n) = (n==1) || (ispower(s=sigma(n), 8) && !(n % sqrtnint(s, 8))); \\ Michel Marcus, May 05 2018

Extensions

a(17)-a(25) from Giovanni Resta, May 04 2018
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