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A321812 Sum of 8th powers of odd divisors of n. 2
1, 1, 6562, 1, 390626, 6562, 5764802, 1, 43053283, 390626, 214358882, 6562, 815730722, 5764802, 2563287812, 1, 6975757442, 43053283, 16983563042, 390626, 37828630724, 214358882, 78310985282, 6562, 152588281251, 815730722, 282472589764 (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).

Eric Weisstein's World of Mathematics, Odd Divisor Function

Index entries for sequences mentioned by Glaisher

FORMULA

a(n) = A013956(A000265(n)) = sigma_8(odd part of n); in particular, a(2^k) = 1 for all k >= 0. - M. F. Hasler, Nov 26 2018

G.f.: Sum_{k>=1} (2*k - 1)^8*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 07 2018

MATHEMATICA

a[n_] := DivisorSum[n, #^8 &, OddQ[#] &]; Array[a, 20] (* Amiram Eldar, Dec 07 2018 *)

PROG

(PARI) apply( A321812(n)=sigma(n>>valuation(n, 2), 8), [1..30]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Column k=8 of A285425.

Cf. A050999, A051000, A051001, A051002, A321810 - A321816 (analog for 2nd .. 12th powers).

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

Sequence in context: A017312 A017432 A017564 * A031579 A288884 A031759

Adjacent sequences:  A321809 A321810 A321811 * A321813 A321814 A321815

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)