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A321808 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^11.

%I A321808 #16 Nov 22 2022 22:01:05
%S A321808 1,-2049,177148,-4192257,48828126,-362976252,1977326744,-8585738241,
%T A321808 31381236757,-100048830174,285311670612,-742649943036,1792160394038,
%U A321808 -4051542498456,8649804864648,-17583591913473,34271896307634,-64300154115093
%N A321808 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^11.
%H A321808 Seiichi Manyama, <a href="/A321808/b321808.txt">Table of n, a(n) for n = 1..10000</a>
%H A321808 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 A321808 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>.
%F A321808 G.f.: Sum_{k>=1} (-1)^(k+1)*k^11*x^k/(1 + x^k). - _Ilya Gutkovskiy_, Dec 22 2018
%F A321808 Multiplicative with a(2^e) = -3*(341*2^(11*e+1) + 1365)/2047, and a(p^e) = (p^(11*e+11) - 1)/(p^11 - 1) for p > 2. - _Amiram Eldar_, Nov 22 2022
%t A321808 a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^11 &]; Array[a, 50] (* _Amiram Eldar_, Nov 22 2022 *)
%o A321808 (PARI) apply( A321808(n)=sumdiv(n, d, (-1)^(n\d-d)*d^11), [1..30]) \\ _M. F. Hasler_, Nov 26 2018
%Y A321808 Column k=11 of A322083.
%Y A321808 Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
%K A321808 sign,mult
%O A321808 1,2
%A A321808 _N. J. A. Sloane_, Nov 23 2018