A347516 Number of divisors of n that are at most n^(1/3).

1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 2

Offset

1,8

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

G.f.: Sum_{k>=1} x^(k^3)/(1 - x^k).

Mathematica

a[n_] := DivisorSum[n, 1 &, # <= n^(1/3) &]; Array[a, 100] (* Amiram Eldar, Sep 04 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^3<=n);
(PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/3), x^k^3/(1-x^k)))

Crossrefs

Cf. A000005, A010057, A038548, A347517.

Sequence in context: A348998 A167967 A160990 * A322357 A160989 A066788

Adjacent sequences: A347513 A347514 A347515 * A347517 A347518 A347519

Keyword

nonn

Author

Seiichi Manyama, Sep 04 2021

Status

approved