A309127 a(n) = n + 2^4 * floor(n/2^4) + 3^4 * floor(n/3^4) + 4^4 * floor(n/4^4) + ...

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139

Offset

1,2

Comments

Partial sums of A300909.

Links

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

Formula

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

a(n) ~ zeta(5/4)*n^(5/4)/5 - n/2. - Vaclav Kotesovec, Aug 30 2021

Mathematica

Table[Sum[k^4 Floor[n/k^4], {k, 1, n}], {n, 1, 75}]
nmax = 75; CoefficientList[Series[1/(1 - x) Sum[k^4 x^(k^4)/(1 - x^(k^4)), {k, 1, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sum(k=1, n, k^4*(n\k^4)); \\ Seiichi Manyama, Aug 30 2021

Crossrefs

Cf. A013938, A024916, A300909, A309125, A309126.

Sequence in context: A023796 A032950 A365684 * A248502 A250039 A132032

Adjacent sequences: A309124 A309125 A309126 * A309128 A309129 A309130

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 13 2019

Status

approved