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%I #14 Nov 11 2022 04:34:10
%S 1,2047,177148,4192255,48828126,362621956,1977326744,8585738239,
%T 31381236757,99951173922,285311670612,742649588740,1792160394038,
%U 4047587844968,8649804864648,17583591913471,34271896307634,64237391641579
%N a(n) = Sum_{d|n} (-1)^(n/d+1)*d^11.
%H Seiichi Manyama, <a href="/A321556/b321556.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&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} k^11*x^k/(1 + x^k). - _Seiichi Manyama_, Nov 25 2018
%F From _Amiram Eldar_, Nov 11 2022: (Start)
%F Multiplicative with a(2^e) = (1023*2^(11*e+1)+1)/2047, and a(p^e) = (p^(11*e+11) - 1)/(p^11 - 1) if p > 2.
%F Sum_{k=1..n} a(k) ~ c * n^12, where c = 2047*zeta(12)/24576 = 0.0833131... . (End)
%t f[p_, e_] := (p^(11*e + 11) - 1)/(p^11 - 1); f[2, e_] := (1023*2^(11*e + 1) + 1)/2047; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* _Amiram Eldar_, Nov 11 2022 *)
%o (PARI) apply( A321556(n)=sumdiv(n, d, (-1)^(n\d-1)*d^11), [1..30]) \\ _M. F. Hasler_, Nov 26 2018
%Y Cf. A321543 - A321565, A321807 - A321836 for similar sequences.
%Y Cf. A013670.
%K nonn,mult
%O 1,2
%A _N. J. A. Sloane_, Nov 23 2018
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