A303999 Numbers whose sum of divisors is the seventh power of one of their divisors.

1, 112890, 120054, 124338, 133998, 137058, 139962, 36705396, 39118548, 52166212, 4661585292, 4677211812, 4851457716, 4968055596, 6168611160, 6232929480, 6236525932, 6261521812, 6311227560, 6362855640, 6430524120, 6468862876, 6488003880, 6500134440, 6506266732

Offset: 1

Author

Paolo P. Lava, May 04 2018

Keywords

• nonn
• easy

Comments

Subset of A048257.

Examples

			Divisors of 112890 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 71, 106, 142, 159, 213, 265, 318, 355, 426, 530, 710, 795, 1065, 1590, 2130, 3763, 7526, 11289, 18815, 22578, 37630, 56445, 112890 and their sum is 279936 = 6^7.
		

Crossrefs

Cf. A000203, A048257, A303123, A303993, A303994, A303995, A303996.

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]^7 then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Select[Range[150000], IntegerQ[t = DivisorSigma[1, #]^(1/7)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *)

PARI

isok(n) = (n==1) || (ispower(s=sigma(n), 7) && !(n % sqrtnint(s, 7))); \\ Michel Marcus, May 05 2018

Extensions

a(11)-a(25) from Giovanni Resta, May 04 2018