A116913 Inverse Moebius transform of pentagonal numbers.
1, 6, 13, 28, 36, 69, 71, 120, 130, 186, 177, 301, 248, 363, 378, 496, 426, 663, 533, 798, 734, 897, 783, 1245, 961, 1254, 1210, 1547, 1248, 1914, 1427, 2016, 1806, 2148, 1926, 2821, 2036, 2685, 2522, 3270, 2502, 3702, 2753, 3801, 3510, 3939, 3291, 5053, 3648
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
Table[Sum[d*(3d - 1)/2, {d, Divisors[n]}], {n, 101}] (* Indranil Ghosh, May 23 2017 *) -
PARI
a(n) = sumdiv(n, d, d*(3*d-1)/2); \\ Michel Marcus, Mar 25 2015
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PARI
a(n) = {my(f = factor(n)); (3 * sigma(f, 2) - sigma(f)) / 2;} \\ Amiram Eldar, Dec 29 2024
Formula
a(n) = Sum_{d|n} d*(3*d-1)/2.
G.f.: Sum_{k>=1} k*(3*k-1)/2*x^k/(1 - x^k). - Ilya Gutkovskiy, May 23 2017
From Amiram Eldar, Dec 29 2024: (Start)
Dirichlet g.f.: zeta(s) * (3*zeta(s-2) - zeta(s-1))/2.
Sum_{k=1..n} a(k) ~ (zeta(3)/2) * n^3. (End)
Extensions
More terms from Michel Marcus, Mar 25 2015