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A321551 a(n) = Sum_{d|n} (-1)^(d-1)*d^12. 2

%I

%S 1,-4095,531442,-16781311,244140626,-2176254990,13841287202,

%T -68736258047,282430067923,-999755863470,3138428376722,-8918293480462,

%U 23298085122482,-56680071092190,129746582562692,-281543712968703,582622237229762,-1156551128144685,2213314919066162,-4096999772640686

%N a(n) = Sum_{d|n} (-1)^(d-1)*d^12.

%H Seiichi Manyama, <a href="/A321551/b321551.txt">Table of n, a(n) for n = 1..10000</a>

%H 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. 4 and p. 8).

%H <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>

%F G.f.: Sum_{k>=1} (-1)^(k-1)*k^12*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Dec 24 2018

%o (PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^12), [1..30]) \\ _M. F. Hasler_, Nov 26 2018

%Y Cf. A321543 - A321565, A321807 - A321836 for similar sequences.

%K sign,mult

%O 1,2

%A _N. J. A. Sloane_, Nov 23 2018

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)