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

1,2

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006218, A048766, A094820, A347516.

Sequence in context: A144769 A165737 A349996 * A358992 A033104 A191325

Adjacent sequences: A347514 A347515 A347516 * A347518 A347519 A347520

Keyword

nonn

Author

Seiichi Manyama, Sep 04 2021

Status

approved