A372625 -id:A372625 - cp's OEIS frontend

A373031 Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k^2) / (1 - x^k).

1, 1, 1, -3, 1, -3, 1, -3, 10, -3, 1, 6, 1, -3, 10, -19, 1, 6, 1, -19, 10, -3, 1, -10, 26, -3, 10, -19, 1, 31, 1, -19, 10, -3, 26, -46, 1, -3, 10, 6, 1, -30, 1, -19, 35, -3, 1, -46, 50, 22, 10, -19, 1, -30, 26, 30, 10, -3, 1, -21, 1, -3, 59, -83, 26, -30, 1, -19, 10, 71

Offset: 1

Ilya Gutkovskiy, May 20 2024

sign

Cf. A038548, A064027, A066839, A095118, A321543, A333781, A333782, A344300, A372625, A373032.

nmax = 70; CoefficientList[Series[Sum[(-1)^(k + 1) k^2 x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(d+1) * d^2.

A373032 Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k*(k+1)) / (1 - x^k).

Original entry on oeis.org

0, 1, 1, 1, 1, -3, 1, -3, 1, -3, 1, 6, 1, -3, 10, -3, 1, 6, 1, -19, 10, -3, 1, -10, 1, -3, 10, -19, 1, 31, 1, -19, 10, -3, 26, -10, 1, -3, 10, 6, 1, -30, 1, -19, 35, -3, 1, -46, 1, 22, 10, -19, 1, -30, 26, 30, 10, -3, 1, -21, 1, -3, 59, -19, 26, -30, 1, -19, 10, 71

Offset: 1

Ilya Gutkovskiy, May 20 2024

sign

Cf. A056924, A064027, A070039, A321543, A333809, A333810, A339353, A344300, A372625, A373031.

nmax = 70; CoefficientList[Series[Sum[(-1)^(k + 1) k^2 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

a(n) = Sum_{d|n, d < sqrt(n)} (-1)^(d+1) * d^2.

cp's OEIS Frontend

A373031 Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k^2) / (1 - x^k).

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