A305321 -id:A305321 - cp's OEIS frontend

A305320 Expansion of Product_{k>=1} (1 - x^sigma(k)).

1, -1, 0, -1, 0, 1, -1, 1, -1, 2, 1, 0, -3, 0, 0, 2, 1, -2, 0, 1, 2, -1, -3, -4, 0, 3, 4, 0, -4, -1, 6, -3, 3, -9, 0, 5, 10, 0, -6, -7, 0, 6, -2, 2, -9, 6, 7, 4, -7, -7, -11, 8, 11, 3, -5, -1, -3, 9, -10, 1, -9, 0, 16, 8, 0, -4, -4, -20, 12, -8, 11, 0, -7, 14, -2

Offset: 0

Seiichi Manyama, May 30 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A000203, A111865, A305321.

with(numtheory):
seq(coeff(series(mul(1-x^sigma(k),k=1..n), x,90),x,n),n=0..80); # Muniru A Asiru, May 31 2018

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

A333045 Expansion of Product_{k>=1} (1 + x^sigma(k)) / (1 - x^sigma(k)).

Original entry on oeis.org

1, 2, 2, 4, 8, 10, 14, 24, 34, 44, 62, 86, 116, 156, 206, 274, 362, 462, 598, 782, 994, 1258, 1606, 2018, 2528, 3178, 3952, 4904, 6094, 7490, 9194, 11322, 13834, 16836, 20518, 24880, 30086, 36366, 43792, 52656, 63250, 75626, 90344, 107926, 128422, 152546

Offset: 0

Vaclav Kotesovec, Mar 06 2020

nonn

Convolution of A111865 and A305321.

Cf. A000203, A111865, A305321.

nmax = 50; CoefficientList[Series[Product[(1 + x^DivisorSigma[1, k])/(1 - x^DivisorSigma[1, k]), {k, 1, nmax}], {x, 0, nmax}], x]

cp's OEIS Frontend

A305320 Expansion of Product_{k>=1} (1 - x^sigma(k)).

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