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A321824 a(n) = Sum_{d|n, d==1 mod 4} d^8 - Sum_{d|n, d==3 mod 4} d^8. 3
1, 1, -6560, 1, 390626, -6560, -5764800, 1, 43040161, 390626, -214358880, -6560, 815730722, -5764800, -2562506560, 1, 6975757442, 43040161, -16983563040, 390626, 37817088000, -214358880, -78310985280, -6560, 152588281251, 815730722 (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)^8*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 06 2018

MATHEMATICA

s[n_, r_] := DivisorSum[n, #^8 &, Mod[#, 4] == r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)

PROG

(PARI) apply( A321824(n)=sumdiv(n>>valuation(n, 2), d, (2-d%4)*d^8), [1..40]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Column k=8 of A322143.

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

Sequence in context: A236898 A252100 A137231 * A043488 A046321 A043456

Adjacent sequences:  A321821 A321822 A321823 * A321825 A321826 A321827

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

EXTENSIONS

Keyword mult from Ilya Gutkovskiy, Dec 06 2018

STATUS

approved

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Last modified June 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)