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

1,2

Comments

Subset of A019423.

Links

Table of n, a(n) for n=1..27.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000203, A019423, A303123, A303993, A303994, A303996.

Sequence in context: A236252 A232262 A048255 * A091329 A261241 A345772

Adjacent sequences: A303992 A303993 A303994 * A303996 A303997 A303998

Keyword

nonn

Author

Paolo P. Lava, May 04 2018

Extensions

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

Status

approved