A292919 Sum of n-th powers of odd divisors of n.

1, 1, 28, 1, 3126, 730, 823544, 1, 387440173, 9765626, 285311670612, 531442, 302875106592254, 678223072850, 437893920912786408, 1, 827240261886336764178, 150094635684419611, 1978419655660313589123980, 95367431640626, 5842587018944528395924761632, 81402749386839761113322

Offset: 1

Author

Ilya Gutkovskiy, Sep 26 2017

Keywords

• nonn
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386
• Index entries for sequences related to sums of divisors

Crossrefs

Diagonal of A285425.

Cf. A000593, A023887, A082245.

Programs

Maple

f:= proc(n) local t,d;
  t:= n/2^padic:-ordp(n,2);
  add(d^n, d = numtheory:-divisors(t));
end proc:
map(f, [$1..30]); # Robert Israel, Sep 27 2017

Mathematica

Rest[Table[SeriesCoefficient[Sum[(2 k - 1)^n x^(2 k - 1)/(1 - x^(2 k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 22}]]
f[n_] := Plus @@ (Select[Divisors[n], OddQ]^n); Array[f, 22] (* Robert G. Wilson v, Sep 26 2017 *)

PARI

a(n) = sumdiv(n, d, if (d%2, d^n)); \\ Michel Marcus, Sep 08 2018

Formula

a(n) = [x^n] Sum_{k>=1} (2*k - 1)^n*x^(2*k-1)/(1 - x^(2*k-1)).

a(2^k) = 1.