A300547 -id:A300547

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A300548

a(n) = [x^n] Product_{d|n} 1/(1 + x^d).

+10
3

1, -1, 0, -2, 0, -2, 0, -2, 0, -5, 1, -2, 1, -2, 0, -14, 0, -2, 1, -2, 0, -18, 0, -2, 0, -7, 1, -23, 0, -2, 6, -2, 0, -26, 1, -26, 4, -2, 0, -30, 0, -2, 6, -2, 1, -286, 0, -2, 0, -9, 7, -38, 0, -2, 8, -38, 1, -42, 1, -2, 7, -2, 0, -493, 0, -44, 9, -2, 0, -50, 10, -2, 0, -2, 1, -698, 1, -50, 12, -2, 0, -239, 1, -2, 10, -56

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

OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10201

Index entries for sequences related to partitions

FORMULA

a(n) = -2 if n is an odd prime (A065091).

MATHEMATICA

Table[SeriesCoefficient[Product[1/(1 + Boole[Mod[n, k] == 0] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 85}]

PROG

(PARI) A300548(n) = if(!n, 1, my(p=1); fordiv(n, d, p /= (1 + 'x^d)); polcoeff(Ser(p, 'x, 1+n), n)); \\ Antti Karttunen, Nov 27 2024

CROSSREFS

Cf. A018818, A033630, A065091, A081362, A300547, A300549.

KEYWORD

sign,changed

AUTHOR

Ilya Gutkovskiy, Mar 08 2018

STATUS

approved

A300549

a(n) = [x^n] Product_{d|n} (1 + x^d)/(1 - x^d).

+10
2

1, 2, 4, 4, 10, 4, 28, 4, 36, 14, 44, 4, 284, 4, 60, 64, 202, 4, 616, 4, 732, 88, 92, 4, 5740, 22, 108, 112, 1404, 4, 10672, 4, 1828, 136, 140, 144, 42622, 4, 156, 160, 22940, 4, 28024, 4, 3420, 3172, 188, 4, 266524, 30, 4344, 208, 4764, 4, 58600, 224, 60204, 232, 236, 4, 3464272, 4, 252, 6052, 27338, 264

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

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..65.

Index entries for sequences related to partitions

FORMULA

a(n) = 4 if n is a prime (A000040).

MATHEMATICA

Table[SeriesCoefficient[Product[(1 + Boole[Mod[n, k] == 0] x^k)/(1 - Boole[Mod[n, k] == 0] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 65}]

CROSSREFS

Cf. A000040, A015128, A018818, A033630, A300547, A300548.