This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372966 #22 May 20 2024 02:28:11
%S A372966 1,241,6481,61681,390001,1561921,5762401,15790321,42521761,93990241,
%T A372966 214344241,399754561,815702161,1388738641,2527596481,4042322161,
%U A372966 6975673921,10247744401,16983432721,24055651681,37346120881,51656962081,78310705441,102337070401
%N A372966 a(n) = sigma_8(n^2)/sigma_4(n^2).
%C A372966 Apparently, a(n) == 1 (mod 240). - _Hugo Pfoertner_, May 20 2024
%H A372966 Amiram Eldar, <a href="/A372966/b372966.txt">Table of n, a(n) for n = 1..10000</a>
%F A372966 a(n) = Sum_{1 <= x_1, x_2, x_3, x_4 <= n} ( n/gcd(x_1, x_2, x_3, x_4, n) )^4.
%F A372966 a(n) = Sum_{d|n} mu(n/d) * (n/d)^4 * sigma_8(d).
%F A372966 From _Amiram Eldar_, May 20 2024: (Start)
%F A372966 Multiplicative with a(p^e) = (p^(8*e + 4) + 1)/(p^4 + 1).
%F A372966 Dirichlet g.f.: zeta(s)*zeta(s-8)/zeta(s-4).
%F A372966 Sum_{k=1..n} a(k) ~ (zeta(9)/(9*zeta(5))) * n^9. (End)
%t A372966 f[p_, e_] := (p^(8*e + 4) + 1)/(p^4 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* _Amiram Eldar_, May 20 2024 *)
%o A372966 (PARI) a(n) = sigma(n^2, 8)/sigma(n^2, 4);
%o A372966 (PARI) a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^4*sigma(d, 8));
%Y A372966 Cf. A057660, A084218, A084220, A108223.
%Y A372966 Cf. A008683, A013956.
%Y A372966 Cf. A372965.
%K A372966 nonn,mult
%O A372966 1,2
%A A372966 _Seiichi Manyama_, May 18 2024