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

%I A081864 N2353 #46 Jan 08 2025 09:27:01
%S A081864 1,244,3126,16808,59293,161052,371294,762744,1419858,2476100,4101152,
%T A081864 6436344,9768751,14408200,20511150,28629152,39296688,52541808,
%U A081864 69343958,90595736,115856202,147008444,185349918,229345008,282492057,346445352,418195494,503448552,604168400
%N A081864 Sum of 5th powers of the divisors of odd numbers: a(n) = sigma_5(2n-1).
%D A081864 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%H A081864 Amiram Eldar, <a href="/A081864/b081864.txt">Table of n, a(n) for n = 1..10000</a>
%H A081864 J. W. L. Glaisher, <a href="https://books.google.com/books?id=bLs9AQAAMAAJ&amp;pg=RA1-PA1">On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares</a>, Quart. J. Math. 38 (1907), 1-62 (see p. 56).
%H A081864 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>.
%F A081864 Sum_{k=1..n} a(k) ~ c * n^6, where c = Pi^6 / 180 = 5.341051... = 3*A333972. - _Amiram Eldar_, Jan 08 2025
%p A081864 with(numtheory); [seq(sigma[5](2*n-1),n=1..100)];
%t A081864 DivisorSigma[5,Range[1,61,2]] (* _Harvey P. Dale_, Jan 12 2016 *)
%o A081864 (PARI) a(n) = sigma(2*n-1, 5); \\ _Michel Marcus_, Aug 17 2019
%o A081864 (Magma) [DivisorSigma(5,2*n-1):n in [1..30]]; // _Marius A. Burtea_, Aug 17 2019
%Y A081864 Cf. A001160, A333972.
%K A081864 nonn
%O A081864 1,2
%A A081864 _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
%E A081864 Definition clarified by _Harvey P. Dale_, Jan 12 2016