A306912 a(n) = 1 + Sum_{k=1..n} Sum_{d|k} mu(k/d)*p(d), where p(d) = number of partitions of d (A000041).
1, 2, 3, 5, 8, 14, 21, 35, 52, 79, 113, 168, 231, 331, 450, 617, 826, 1122, 1469, 1958, 2540, 3315, 4260, 5514, 6995, 8946, 11280, 14260, 17840, 22404, 27790, 34631, 42749, 52834, 64846, 79708, 97234, 118870, 144394, 175476, 212170, 256752, 309007, 372267, 446437, 535368
Offset: 0
Keywords
Programs
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Mathematica
Table[1 + Sum[Sum[MoebiusMu[k/d] PartitionsP[d], {d, Divisors[k]}], {k, 1, n}], {n, 0, 45}] -
PARI
a(n) = 1 + sum(k=1, n, sumdiv(k, d, moebius(k/d)*numbpart(d))); \\ Michel Marcus, Mar 16 2019
Formula
a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(3/2)*Pi*sqrt(n)). - Vaclav Kotesovec, Mar 17 2019
Comments