A303995 Numbers whose sum of divisors is the fifth power of one of their divisors.

1, 3210, 3498, 3882, 6453804, 7873684, 7943640, 8028120, 8099880, 9112230, 9561990, 10079430, 182626920, 192651480, 196192920, 199939320, 200271960, 201632760, 203289240, 206367480, 206645880, 207815160, 208955160, 210368760, 210406680, 210717720, 211645560

Offset: 1

Author

Paolo P. Lava, May 04 2018

Keywords

• nonn

Comments

Subset of A019423.

Examples

			Divisors of 3210 are 1, 2, 3, 5, 6, 10, 15, 30, 107, 214, 321, 535, 642, 1070, 1605, 3210 and their sum is 7776 = 6^5.
		

Crossrefs

Cf. A000203, A019423, A303123, A303993, A303994, 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]^5 then print(n); break; fi; od; od; end: P(10^9);

Mathematica

Select[Range[10^4], IntegerQ[t = DivisorSigma[1, #]^(1/5)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *)

PARI

isok(n) = (n==1) || (ispower(s=sigma(n), 5) && !(n % sqrtnint(s, 5))); \\ Michel Marcus, May 05 2018

Extensions

a(13)-a(27) from Giovanni Resta, May 04 2018