A334925 G.f.: Sum_{k>=1} x^(k*(k^2 + 1)/2) / (1 - x^(k*(k^2 + 1)/2)).

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

Offset

1,5

Comments

Number of divisors of n of the form k*(k^2 + 1)/2 (A006003).

Links

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

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 * (A248177 + A001620) = 1.343731... . - Amiram Eldar, Jan 02 2024

Mathematica

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

Crossrefs

Cf. A006003, A007862, A279495, A300409, A334926.

Cf. A001620, A248177.

Sequence in context: A025896 A050432 A343747 * A247090 A030346 A030336

Adjacent sequences: A334922 A334923 A334924 * A334926 A334927 A334928

Keyword

nonn

Author

Ilya Gutkovskiy, May 16 2020

Status

approved