OFFSET
1,2
COMMENTS
Partial sums of A035316.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Vaclav Kotesovec, Plot of a(n)/n^(3/2) for n = 1..10000
FORMULA
G.f.: (1/(1 - x)) * Sum_{k>=1} k^2 * x^(k^2)/(1 - x^(k^2)).
a(n) ~ zeta(3/2)*n^(3/2)/3 - n/2. - Vaclav Kotesovec, Aug 30 2021
MATHEMATICA
Table[Sum[k^2 Floor[n/k^2], {k, 1, n}], {n, 1, 66}]
nmax = 66; CoefficientList[Series[1/(1 - x) Sum[k^2 x^(k^2)/(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sum(k=1, n, k^2*(n\k^2)); \\ Seiichi Manyama, Aug 30 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 13 2019
STATUS
approved