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A321807 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^10.

%I A321807 #18 Nov 22 2022 22:00:57
%S A321807 1,-1025,59050,-1047553,9765626,-60526250,282475250,-1072692225,
%T A321807 3486843451,-10009766650,25937424602,-61858004650,137858491850,
%U A321807 -289537131250,576660215300,-1098436836353,2015993900450,-3574014537275,6131066257802
%N A321807 a(n) = Sum_{d divides n} (-1)^(d + n/d) * d^10.
%H A321807 Seiichi Manyama, <a href="/A321807/b321807.txt">Table of n, a(n) for n = 1..10000</a>
%H A321807 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 A321807 <a href="/index/Ge#Glaisher">Index entries for sequences mentioned by Glaisher</a>.
%F A321807 G.f.: Sum_{k>=1} (-1)^(k+1)*k^10*x^k/(1 + x^k). - _Ilya Gutkovskiy_, Dec 22 2018
%F A321807 Multiplicative with a(2^e) = -(511*2^(10*e+1) + 2047)/1023, and a(p^e) = (p^(10*e+10) - 1)/(p^10 - 1) for p > 2. - _Amiram Eldar_, Nov 22 2022
%t A321807 a[n_] := DivisorSum[n, (-1)^(# + n/#)*#^10 &]; Array[a, 50] (* _Amiram Eldar_, Nov 22 2022 *)
%o A321807 (PARI) apply( A321807(n)=sumdiv(n, d, (-1)^(d-n\d)*d^10), [1..30]) \\ _M. F. Hasler_, Nov 26 2018
%Y A321807 Column k=10 of A322083.
%Y A321807 Cf. A321543 - A321565, A321808 - A321836 for similar sequences.
%K A321807 sign,mult
%O A321807 1,2
%A A321807 _N. J. A. Sloane_, Nov 23 2018