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 A373040 #14 Jan 03 2025 05:21:17
%S A373040 0,1,6,17,50,79,196,273,492,651,1210,1247,2366,2549,3656,4369,6936,
%T A373040 6397,10830,10267,14314,15731,23276,19935,31300,30759,39858,40197,
%U A373040 58870,47529,76880,69905,88336,90169,117846,100877,156066,140791,172724,164123,235340,186083
%N A373040 a(n) = (A084218(n) - 1)/12.
%H A373040 Amiram Eldar, <a href="/A373040/b373040.txt">Table of n, a(n) for n = 1..10000</a>
%F A373040 From _Amiram Eldar_, Jan 03 2025: (Start)
%F A373040 Dirichlet g.f.: (zeta(s-4)/zeta(s-2) - zeta(s))/12.
%F A373040 Sum_{k=1..n} a(k) ~ c * n^5, where c = zeta(5)/(60*zeta(3)) = 0.0143771... . (End)
%t A373040 f[p_, e_] := (p^(4*e + 2) + 1)/(p^2 + 1); a[1] = 0; a[n_] := (Times @@ f @@@ FactorInteger[n] - 1) / 12; Array[a, 35] (* _Amiram Eldar_, Jan 03 2025 *)
%o A373040 (PARI) a(n) = (sigma(n^2, 4)/sigma(n^2, 2) - 1)/12
%Y A373040 Cf. A000290, A001157, A001159, A084218, A372966, A373039.
%Y A373040 Cf. A002117, A013663.
%K A373040 nonn,easy
%O A373040 1,3
%A A373040 _Hugo Pfoertner_, May 20 2024