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

1,2

Comments

Subset of A048257.

Links

Table of n, a(n) for n=1..25.

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A269887 A269766 A177275 * A252036 A103113 A179922

Adjacent sequences: A303996 A303997 A303998 * A304000 A304001 A304002

Keyword

nonn,easy

Author

Paolo P. Lava, May 04 2018

Extensions

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

Status

approved