

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
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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), 162 (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*k1)/(1  x^(2*k1)).  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



