A305321 Expansion of Product_{k>=1} (1 + x^sigma(k)).

1, 1, 0, 1, 2, 1, 1, 3, 3, 2, 3, 4, 5, 6, 6, 8, 9, 8, 12, 15, 14, 17, 21, 20, 24, 31, 30, 34, 42, 41, 46, 59, 63, 67, 76, 83, 94, 104, 112, 131, 144, 144, 170, 198, 201, 226, 261, 268, 291, 337, 361, 392, 437, 465, 511, 567, 607, 673, 736, 775, 861, 946, 1000

Offset: 0

Author

Seiichi Manyama, May 30 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama)

Crossrefs

Cf. A000203, A111865, A305320.

Programs

Maple

with(numtheory):
seq(coeff(series(mul(1+x^sigma(k),k=1..n), x,80),x,n),n=0..70); # Muniru A Asiru, May 31 2018

Mathematica

nmax = 100; CoefficientList[Series[Product[1 + x^DivisorSigma[1, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 03 2018 *)

PARI

N=99; x='x+O('x^N); Vec(prod(k=1, N, 1+x^sigma(k)))