A321286 -id:A321286 - cp's OEIS frontend

A321285 Expansion of Product_{1 <= i < j} 1/(1 - x^(i*j)).

1, 0, 1, 1, 2, 2, 5, 4, 9, 9, 16, 17, 31, 31, 52, 59, 89, 101, 154, 172, 254, 294, 412, 483, 675, 782, 1070, 1265, 1686, 1996, 2647, 3121, 4086, 4854, 6252, 7442, 9534, 11306, 14360, 17092, 21489, 25566, 31989, 37981, 47224, 56123, 69283, 82290, 101185, 119930, 146768

Offset: 0

Seiichi Manyama, Nov 02 2018

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Transforms

Cf. A056924, A182269, A321286.

nmax = 50; CoefficientList[Series[Product[1/(1 - x^k)^Floor[DivisorSigma[0, k]/2], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 02 2018 *)

Euler transform of A056924.

G.f.: Product_{k>0} 1/(1 - x^k)^A056924(k).

A321300 Expansion of Product_{1 <= i < j} (1 - x^(i*j)).

Original entry on oeis.org

1, 0, -1, -1, -1, 0, -1, 1, 1, 2, 2, 2, 0, 0, 2, -2, -1, -3, -1, -4, -4, -4, -1, -1, -2, 0, 3, 7, 3, 4, 5, 7, 5, 8, 3, 2, 4, 1, -6, -2, -8, -8, -12, -9, -9, -11, -13, -12, -6, -8, -6, -8, 11, 5, 6, 8, 18, 12, 22, 21, 28, 26, 28, 12, 21, 22, 11, 0, 0, -4, -18, -17, -38

Offset: 0

Seiichi Manyama, Nov 03 2018

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Convolution inverse of A321285.

Cf. A056924, A321286, A321299.

nmax = 100; CoefficientList[Series[Product[(1 - x^k)^Floor[DivisorSigma[0, k]/2], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 03 2018 *)

G.f.: Product_{k>0} (1 - x^k)^A056924(k).

cp's OEIS Frontend

A321285 Expansion of Product_{1 <= i < j} 1/(1 - x^(i*j)).

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