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

0,2

Comments

Partial sums of A000837.

Links

Table of n, a(n) for n=0..45.

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(3/2)*Pi*sqrt(n)). - Vaclav Kotesovec, Mar 17 2019

Mathematica

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

Prog

(PARI) a(n) = 1 + sum(k=1, n, sumdiv(k, d, moebius(k/d)*numbpart(d))); \\ Michel Marcus, Mar 16 2019

Crossrefs

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

Sequence in context: A082931 A034413 A034416 * A212607 A056366 A000046

Adjacent sequences: A306909 A306910 A306911 * A306913 A306914 A306915

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2019

Status

approved