A081864 Sum of 5th powers of the divisors of odd numbers: a(n) = sigma_5(2n-1).

1, 244, 3126, 16808, 59293, 161052, 371294, 762744, 1419858, 2476100, 4101152, 6436344, 9768751, 14408200, 20511150, 28629152, 39296688, 52541808, 69343958, 90595736, 115856202, 147008444, 185349918, 229345008, 282492057, 346445352, 418195494, 503448552, 604168400

Offset: 1

Author

N. J. A. Sloane. This sequence was in the 1973 "Handbook", but then was deleted from the database because of confusion with A002594. Resubmitted by Benoit Cloitre, Apr 12 2003. Entry revised by N. J. A. Sloane, Jun 10 2012

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

• Amiram Eldar, 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. 56).
• Index entries for sequences mentioned by Glaisher.

Crossrefs

Cf. A001160, A333972.

Programs

Magma

[DivisorSigma(5,2*n-1):n in [1..30]]; // Marius A. Burtea, Aug 17 2019

Maple

with(numtheory); [seq(sigma[5](2*n-1),n=1..100)];

Mathematica

DivisorSigma[5,Range[1,61,2]] (* Harvey P. Dale, Jan 12 2016 *)

PARI

a(n) = sigma(2*n-1, 5); \\ Michel Marcus, Aug 17 2019

Formula

Sum_{k=1..n} a(k) ~ c * n^6, where c = Pi^6 / 180 = 5.341051... = 3*A333972. - Amiram Eldar, Jan 08 2025

Extensions

Definition clarified by Harvey P. Dale, Jan 12 2016