A347517 Partial sums of A347516.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 22, 24, 25, 27, 28, 30, 31, 33, 34, 36, 38, 40, 41, 44, 45, 47, 49, 51, 52, 55, 56, 58, 60, 62, 63, 66, 67, 69, 71, 73, 74, 77, 78, 80, 82, 84, 85, 88, 89, 91, 93, 95, 96, 99, 100, 102, 104, 107, 108, 111, 112, 115, 117, 119, 120, 124, 125, 127, 129, 132, 133, 136

Offset: 1

Author

Seiichi Manyama, Sep 04 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A006218, A048766, A094820, A347516.

Programs

Mathematica

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

PARI

N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/3), x^k^3/(1-x^k))/(1-x))

PARI

a(n) = sum(k=1, n, sumdiv(k, d, d^3<=k)); \\ Michel Marcus, Sep 05 2021

Formula

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