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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 28 05:17 EST 2020. Contains 338699 sequences. (Running on oeis4.)