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A321826 a(n) = Sum_{d|n, d==1 mod 4} d^10 - Sum_{d|n, d==3 mod 4} d^10. 3
1, 1, -59048, 1, 9765626, -59048, -282475248, 1, 3486725353, 9765626, -25937424600, -59048, 137858491850, -282475248, -576640684048, 1, 2015993900450, 3486725353, -6131066257800, 9765626, 16679598443904, -25937424600, -41426511213648, -59048, 95367441406251, 137858491850 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

a(n) = a(A000265(n)). - M. F. Hasler, Nov 26 2018

G.f.: Sum_{k>=1} (-1)^(k-1)*(2*k - 1)^10*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 22 2018

MATHEMATICA

s[n_, r_] := DivisorSum[n, #^10 &, Mod[#, 4] == r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)

PROG

(PARI) apply( A321826(n)=sumdiv(n>>valuation(n, 2), d, (2-d%4)*d^10), [1..40]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Column k=10 of A322143.

Cf. A321543 - A321565, A321807 - A321836 for similar sequences.

Sequence in context: A217603 A205233 A235953 * A255893 A046323 A017081

Adjacent sequences:  A321823 A321824 A321825 * A321827 A321828 A321829

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified September 21 02:29 EDT 2020. Contains 337266 sequences. (Running on oeis4.)