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A321836 a(n) = Sum_{d|n, n/d==1 mod 4} d^12 - Sum_{d|n, n/d==3 mod 4} d^12. 56
1, 4096, 531440, 16777216, 244140626, 2176778240, 13841287200, 68719476736, 282429005041, 1000000004096, 3138428376720, 8916083671040, 23298085122482, 56693912371200, 129746094281440, 281474976710656, 582622237229762, 1156829204647936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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^12*x^k/(1 + x^(2*k)). - Ilya Gutkovskiy, Nov 26 2018

MATHEMATICA

s[n_, r_] := DivisorSum[n, #^12 &, Mod[n/#, 4]==r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)

PROG

(PARI) apply( a(n)=sumdiv(n, d, if(bittest(n\d, 0), (2-n\d%4)*d^12)), [1..30]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Cf. A321543 - A321565, A321807 - A321835 for similar sequences.

Sequence in context: A232961 A223966 A195660 * A016902 A017688 A008456

Adjacent sequences:  A321833 A321834 A321835 * A321837 A321838 A321839

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified December 14 01:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)