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A321816 Sum of 12th powers of odd divisors of n. 8
1, 1, 531442, 1, 244140626, 531442, 13841287202, 1, 282430067923, 244140626, 3138428376722, 531442, 23298085122482, 13841287202, 129746582562692, 1, 582622237229762, 282430067923, 2213314919066162, 244140626, 7355841353205284, 3138428376722 (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) = A013960(A000265(n)) = sigma_12(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)^12*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 22 2018

MATHEMATICA

a[n_] := DivisorSum[n, #^12&, OddQ[#]&]; Array[a, 20] (* Amiram Eldar, Dec 07 2018 *)

PROG

(PARI) apply( A321816(n)=sigma(n>>valuation(n, 2), 12), [1..30]) \\ M. F. Hasler, Nov 26 2018

CROSSREFS

Column k=12 of A285425.

Cf. A050999, A051000, A051001, A051002, A321810 - A321815 (analog for 2nd .. 11th powers).

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

Sequence in context: A017316 A017436 A017568 * A237480 A081637 A010037

Adjacent sequences:  A321813 A321814 A321815 * A321817 A321818 A321819

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

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Last modified January 23 16:48 EST 2020. Contains 331173 sequences. (Running on oeis4.)