A334924 G.f.: Sum_{k>=1} x^(k^2*(k + 1)/2) / (1 - x^(k^2*(k + 1)/2)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1

Offset

1,6

Comments

Number of pentagonal pyramidal numbers (A002411) dividing n.

Links

Table of n, a(n) for n=1..100.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number.

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/3 - 2 = A195055 - 2 = 1.289868... . - Amiram Eldar, Jan 02 2024

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k^2 (k + 1)/2)/(1 - x^(k^2 (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A002411, A007862, A195055, A279495, A279496, A279497.

Sequence in context: A334926 A305936 A339790 * A211111 A074971 A344008

Adjacent sequences: A334921 A334922 A334923 * A334925 A334926 A334927

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2020

Status

approved