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A321550 a(n) = Sum_{d|n} (-1)^(d-1)*d^11.

%I A321550 #18 Nov 04 2022 10:47:41
%S A321550 1,-2047,177148,-4196351,48828126,-362621956,1977326744,-8594130943,
%T A321550 31381236757,-99951173922,285311670612,-743375186948,1792160394038,
%U A321550 -4047587844968,8649804864648,-17600780175359,34271896307634,-64237391641579,116490258898220,-204899955368226,350279478046112
%N A321550 a(n) = Sum_{d|n} (-1)^(d-1)*d^11.
%H A321550 Seiichi Manyama, <a href="/A321550/b321550.txt">Table of n, a(n) for n = 1..10000</a>
%H A321550 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 A321550 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>.
%F A321550 G.f.: Sum_{k>=1} (-1)^(k-1)*k^11*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Dec 24 2018
%F A321550 Multiplicative with a(2^e) = 2 - (2^(11*e + 11) - 1)/2047, and a(p^e) = (p^(11*e + 11) - 1)/(p^11 - 1) for p > 2. - _Amiram Eldar_, Nov 04 2022
%t A321550 f[p_, e_] := (p^(11*e + 11) - 1)/(p^11 - 1); f[2, e_] := 2 - (2^(11*e + 11) - 1)/2047; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* _Amiram Eldar_, Nov 04 2022 *)
%o A321550 (PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^11), [1..30]) \\ _M. F. Hasler_, Nov 26 2018
%Y A321550 Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
%K A321550 sign,mult
%O A321550 1,2
%A A321550 _N. J. A. Sloane_, Nov 23 2018