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%I #17 Nov 04 2022 10:47:25
%S 1,-127,2188,-16511,78126,-277876,823544,-2113663,4785157,-9922002,
%T 19487172,-36126068,62748518,-104590088,170939688,-270549119,
%U 410338674,-607714939,893871740,-1289938386,1801914272,-2474870844,3404825448,-4624694644,6103593751,-7969061786,10465138360,-13597534984,17249876310
%N a(n) = Sum_{d|n} (-1)^(d-1)*d^7.
%H Seiichi Manyama, <a href="/A321546/b321546.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} (-1)^(k-1)*k^7*x^k/(1 - x^k). - _Ilya Gutkovskiy_, Dec 23 2018
%F Multiplicative with a(2^e) = 2 - (2^(7*e + 7) - 1)/127, and a(p^e) = (p^(7*e + 7) - 1)/(p^7 - 1) for p > 2. - _Amiram Eldar_, Nov 04 2022
%t f[p_, e_] := (p^(7*e + 7) - 1)/(p^7 - 1); f[2, e_] := 2 - (2^(7*e + 7) - 1)/127; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* _Amiram Eldar_, Nov 04 2022 *)
%o (PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^7), [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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