A303996 Numbers whose sum of divisors is the sixth power of one of their divisors.

1, 17490, 19410, 22578, 2823492, 162523452, 165982908, 216731788, 221416468, 221940628, 226768440, 230365560, 232815480, 234896520, 238942920, 240737160, 241362120, 242067720, 242454120, 242655720, 258182910, 264254670, 268298190, 272819070, 277297710, 286008510

Offset

1,2

Comments

Subset of A019424.

Links

Table of n, a(n) for n=1..26.

Example

Divisors of 17490 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 53, 55, 66, 106, 110, 159, 165, 265, 318, 330, 530, 583, 795, 1166, 1590, 1749, 2915, 3498, 5830, 8745, 17490 and their sum is 46656 = 6^6.

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]^6 then print(n); break; fi; od; od; end: P(10^9);

Prog

(PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 6) && !(n % sqrtnint(s, 6))); \\ Michel Marcus, May 05 2018

Crossrefs

Cf. A000203, A019424, A303123, A303993, A303994, A303995.

Sequence in context: A043875 A236806 A048256 * A251641 A251638 A234562

Adjacent sequences: A303993 A303994 A303995 * A303997 A303998 A303999

Keyword

nonn,easy

Author

Paolo P. Lava, May 04 2018

Status

approved