%I #10 Jan 08 2025 09:27:11
%S 0,1,27,257,1625,6508,24010,65793,177174,391626,893101,1665644,
%T 3398759,5786411,10531652,16843009,29065308,42698935,70764303,
%U 100231882,155608837,215237342,326294606,426404460,634767250,819100920,1162438641,1480961067,2084357107,2538128133
%N a(n) = (A372966(n) - 1)/240.
%H Amiram Eldar, <a href="/A373039/b373039.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Jan 08 2025: (Start)
%F Dirichlet g.f.: zeta(s) * (zeta(s-8)/zeta(s-4) - 1)/240.
%F Sum_{k=1..n} a(k) ~ c * n^9, where c = zeta(9)/(2160*zeta(5)) = 0.000447372... . (End)
%t f[p_, e_] := (p^(8*e + 4) + 1)/(p^4 + 1); a[1] = 0; a[n_] := (Times @@ f @@@ FactorInteger[n] - 1) / 240; Array[a, 30] (* _Amiram Eldar_, Jan 08 2025 *)
%o (PARI) a(n) = (sigma(n^2, 8)/sigma(n^2, 4)-1)/240
%Y Cf. A000290, A001159, A013956.
%K nonn
%O 1,3
%A _Hugo Pfoertner_, May 20 2024