A309126 a(n) = n + 2^3 * floor(n/2^3) + 3^3 * floor(n/3^3) + 4^3 * floor(n/4^3) + ...

1, 2, 3, 4, 5, 6, 7, 16, 17, 18, 19, 20, 21, 22, 23, 32, 33, 34, 35, 36, 37, 38, 39, 48, 49, 50, 78, 79, 80, 81, 82, 91, 92, 93, 94, 95, 96, 97, 98, 107, 108, 109, 110, 111, 112, 113, 114, 123, 124, 125, 126, 127, 128, 156, 157, 166, 167, 168, 169, 170, 171, 172, 173, 246, 247, 248, 249, 250, 251, 252

Offset

1,2

Comments

Partial sums of A113061.

Links

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

Formula

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

a(n) ~ zeta(4/3)*n^(4/3)/4 - n/2. - Vaclav Kotesovec, Aug 30 2021

Mathematica

Table[Sum[k^3 Floor[n/k^3], {k, 1, n}], {n, 1, 70}]
nmax = 70; CoefficientList[Series[1/(1 - x) Sum[k^3 x^(k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sum(k=1, n, k^3*(n\k^3)); \\ Seiichi Manyama, Aug 30 2021

Crossrefs

Cf. A013937, A024916, A113061, A309125, A309127.

Sequence in context: A308334 A161673 A368533 * A371289 A004836 A039030

Adjacent sequences: A309123 A309124 A309125 * A309127 A309128 A309129

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 13 2019

Status

approved