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A321829 a(n) = Sum_{d|n, n/d==1 mod 4} d^5 - Sum_{d|n, n/d==3 mod 4} d^5. 3
1, 32, 242, 1024, 3126, 7744, 16806, 32768, 58807, 100032, 161050, 247808, 371294, 537792, 756492, 1048576, 1419858, 1881824, 2476098, 3201024, 4067052, 5153600, 6436342, 7929856, 9768751, 11881408, 14290100, 17209344, 20511150, 24207744, 28629150, 33554432, 38974100, 45435456, 52535556 (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^5*x^k/(1 + x^(2*k)). - Ilya Gutkovskiy, Nov 26 2018

Multiplicative with a(p^e) = round(p^(5e+5)/(p^5 + p%4 - 2)), where p%4 is the remainder of p modulo 4. (Following R. Israel in A321833.) - M. F. Hasler, Nov 26 2018

MATHEMATICA

s[n_, r_] := DivisorSum[n, # ^5 &, Mod[n/#, 4]==r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)

PROG

(PARI) apply( A321829(n)=factorback(apply(f->f[1]^(5*f[2]+5)\/(f[1]^5+f[1]%4-2), Col(factor(n)))), [1..40]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

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

Sequence in context: A333268 A060622 A118999 * A111450 A070332 A111442

Adjacent sequences:  A321826 A321827 A321828 * A321830 A321831 A321832

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified October 27 15:27 EDT 2020. Contains 338035 sequences. (Running on oeis4.)