A309125 a(n) = n + 2^2 * floor(n/2^2) + 3^2 * floor(n/3^2) + 4^2 * floor(n/4^2) + ...
1, 2, 3, 8, 9, 10, 11, 16, 26, 27, 28, 33, 34, 35, 36, 57, 58, 68, 69, 74, 75, 76, 77, 82, 108, 109, 119, 124, 125, 126, 127, 148, 149, 150, 151, 201, 202, 203, 204, 209, 210, 211, 212, 217, 227, 228, 229, 250, 300, 326, 327, 332, 333, 343, 344, 349, 350, 351, 352, 357, 358, 359, 369, 454, 455, 456
Offset: 1
Keywords
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
Programs
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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 -
PARI
a(n) = sum(k=1, n, k^2*(n\k^2)); \\ Seiichi Manyama, Aug 30 2021
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
Comments