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A321814 Sum of 10th powers of odd divisors of n. 2
1, 1, 59050, 1, 9765626, 59050, 282475250, 1, 3486843451, 9765626, 25937424602, 59050, 137858491850, 282475250, 576660215300, 1, 2015993900450, 3486843451, 6131066257802, 9765626, 16680163512500, 25937424602, 41426511213650, 59050 (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) = A013958(A000265(n)) = sigma_10(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)^10*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 07 2018

MATHEMATICA

a[n_] := DivisorSum[n, #^10 &, OddQ[#] &]; Array[a, 20] (* Amiram Eldar, Dec 07 2018 *)

PROG

(PARI) apply( A321814(n)=sigma(n>>valuation(n, 2), 10), [1..30]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Column k=10 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: A017314 A017434 A017566 * A288886 A210172 A224972

Adjacent sequences:  A321811 A321812 A321813 * A321815 A321816 A321817

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)