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

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

1,2

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

Links

Table of n, a(n) for n=1..25.

Example

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.

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);

Prog

(PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 8) && !(n % sqrtnint(s, 8))); \\ Michel Marcus, May 05 2018

Crossrefs

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

Sequence in context: A209515 A106779 A106780 * A206412 A235257 A185928

Adjacent sequences: A303997 A303998 A303999 * A304001 A304002 A304003

Keyword

nonn

Author

Paolo P. Lava, May 04 2018

Extensions

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

Status

approved