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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). 0

%I

%S 1,2,3,5,8,14,21,35,52,79,113,168,231,331,450,617,826,1122,1469,1958,

%T 2540,3315,4260,5514,6995,8946,11280,14260,17840,22404,27790,34631,

%U 42749,52834,64846,79708,97234,118870,144394,175476,212170,256752,309007,372267,446437,535368

%N a(n) = 1 + Sum_{k=1..n} Sum_{d|k} mu(k/d)*p(d), where p(d) = number of partitions of d (A000041).

%C Partial sums of A000837.

%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(3/2)*Pi*sqrt(n)). - _Vaclav Kotesovec_, Mar 17 2019

%t Table[1 + Sum[Sum[MoebiusMu[k/d] PartitionsP[d], {d, Divisors[k]}], {k, 1, n}], {n, 0, 45}]

%o (PARI) a(n) = 1 + sum(k=1, n, sumdiv(k, d, moebius(k/d)*numbpart(d))); \\ _Michel Marcus_, Mar 16 2019

%Y Cf. A000041, A000070, A000837, A008683, A036469.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Mar 16 2019

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Last modified September 27 14:55 EDT 2020. Contains 337383 sequences. (Running on oeis4.)