A347526 Number of divisors of n that are at most n^(1/4).

1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 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

Offset

1,16

Links

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

Formula

G.f.: Sum_{k>=1} x^(k^4)/(1 - x^k).

Mathematica

a[n_] := DivisorSum[n, 1 &, # <= n^(1/4) &]; Array[a, 100] (* Amiram Eldar, Sep 05 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^4<=n);
(PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/4), x^k^4/(1-x^k)))

Crossrefs

Cf. A000005, A038548, A063775, A347516, A347527.

Sequence in context: A040001 A134451 A229217 * A167965 A270370 A167966

Adjacent sequences: A347523 A347524 A347525 * A347527 A347528 A347529

Keyword

nonn

Author

Seiichi Manyama, Sep 05 2021

Status

approved