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 A372996 #16 May 20 2024 02:30:00
%S A372996 1,22,183,704,2605,4026,14707,22548,44469,57310,147631,128832,344773,
%T A372996 323554,476715,721596,1340977,978318,2352295,1833920,2691381,3247882,
%U A372996 6168163,4126284,8140625,7585006,10806147,10353728,19827445,10487730,27734491,23091212,27016473
%N A372996 a(n) = Sum_{k=1..n} sigma_2( (n/gcd(k,n))^2 ).
%H A372996 Seiichi Manyama, <a href="/A372996/b372996.txt">Table of n, a(n) for n = 1..10000</a>
%F A372996 a(n) = Sum_{d|n} phi(d) * sigma_2(d^2).
%F A372996 From _Amiram Eldar_, May 20 2024: (Start)
%F A372996 Multiplicative with a(p^e) = (p^(5*e+7) - p^(5*e+6) - p^(e+5) + p^e + p^6 - p^2) / ((p^2 - 1) * (p^5 - 1)).
%F A372996 Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(5) * zeta(6) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4 - 1/p^6 + 1/p^7) = 0.71416166953252012639... . (End)
%t A372996 a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[2, #^2] &]; Array[a, 100] (* _Amiram Eldar_, May 20 2024 *)
%o A372996 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^2, 2));
%Y A372996 Cf. A062380, A372227.
%Y A372996 Cf. A013663, A013664.
%K A372996 nonn,mult
%O A372996 1,2
%A A372996 _Seiichi Manyama_, May 19 2024