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A284926 a(n) = Sum_{d|n} (-1)^(n/d+1)*d^5. 9
1, 31, 244, 991, 3126, 7564, 16808, 31711, 59293, 96906, 161052, 241804, 371294, 521048, 762744, 1014751, 1419858, 1838083, 2476100, 3097866, 4101152, 4992612, 6436344, 7737484, 9768751, 11510114, 14408200, 16656728, 20511150, 23645064, 28629152, 32472031, 39296688 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Multiplicative because this sequence is the Dirichlet convolution of A000584 and A062157 which are both multiplicative. - Andrew Howroyd, Jul 20 2018

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

Index entries for sequences mentioned by Glaisher

FORMULA

G.f.: Sum_{k>=1} k^5*x^k/(1 + x^k). - Ilya Gutkovskiy, Apr 07 2017

MATHEMATICA

Table[Sum[(-1)^(n/d + 1)*d^5, {d, Divisors[n]}], {n, 50}] (* Indranil Ghosh, Apr 06 2017 *)

PROG

(PARI) a(n) = sumdiv(n, d, (-1)^(n/d + 1)*d^5); \\ Indranil Ghosh, Apr 06 2017

(Python)

from sympy import divisors

print [sum([(-1)**(n/d + 1)*d**5 for d in divisors(n)]) for n in range(1, 51)] # Indranil Ghosh, Apr 06 2017

CROSSREFS

Sum_{d|n} (-1)^(n/d+1)*d^k: A000593 (k=1), A078306 (k=2), A078307 (k=3), A284900 (k=4), this sequence (k=5), A284927 (k=6).

Cf. A000584, A062157.

Sequence in context: A024003 A258807 A221848 * A321544 A147963 A027846

Adjacent sequences:  A284923 A284924 A284925 * A284927 A284928 A284929

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, Apr 06 2017

EXTENSIONS

Keyword:mult added by Andrew Howroyd, Jul 23 2018

STATUS

approved

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Last modified February 28 06:55 EST 2020. Contains 332321 sequences. (Running on oeis4.)