A289384 Numbers k such that the sum of the divisors of k is of the form m^3 + 1.

1, 12, 68, 82, 100, 730, 886, 1089, 1241, 1252, 1352, 1440, 1908, 2804, 2947, 3274, 5598, 6078, 7414, 9123, 10135, 10164, 10804, 10809, 11143, 12756, 13456, 13468, 15004, 21025, 23810, 24642, 25123, 26912, 26983, 34976, 37020, 40477, 45946, 48126, 55964, 56764

Offset: 1

Author

Michel Lagneau, Jul 04 2017

Keywords

• nonn

Comments

Perfect squares in the sequence are 1, 100, 1089, 13456, 21025, ...

Examples

			730 is in the sequence because sigma(730) = 1332 = 11^3 + 1.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1510

Crossrefs

Cf. A000203, A001093, A289290.

Programs

Maple

a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1)) while (t->t<>
      iroot(t, 3)^3)(numtheory[sigma](k)-1) do od; k
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Jul 04 2017

Mathematica

fQ[n_] := ! PrimeQ@n && Block[{sd = DivisorSigma[1, n]}, IntegerQ[(sd - 1)^(1/3)]]; Select[Range@59323, fQ] (* Robert G. Wilson v, Jul 05 2017 *)

PARI

isok(n) = ispower(sigma(n)-1, 3); \\ Michel Marcus, Jul 05 2017

Extensions

More terms from Alois P. Heinz, Jul 04 2017