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

Author

Paolo P. Lava, May 04 2018

Keywords

• nonn
• easy

Comments

Subset of A019424.

Examples

			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.
		

Crossrefs

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

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

PARI

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