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 A372227 #37 May 20 2024 02:30:12
%S A372227 1,8,27,70,125,216,343,578,753,1000,1331,1890,2197,2744,3375,4666,
%T A372227 4913,6024,6859,8750,9261,10648,12167,15606,15745,17576,20427,24010,
%U A372227 24389,27000,29791,37418,35937,39304,42875,52710,50653,54872,59319,72250,68921,74088
%N A372227 a(n) = Sum_{k=1..n} sigma( (n/gcd(k,n))^2 ).
%H A372227 Seiichi Manyama, <a href="/A372227/b372227.txt">Table of n, a(n) for n = 1..10000</a>
%F A372227 If k is squarefree (cf. A005117) then a(k) = k^3.
%F A372227 a(n) = Sum_{d|n} phi(d) * sigma(d^2).
%F A372227 From _Amiram Eldar_, May 20 2024: (Start)
%F A372227 Multiplicative with a(p^e) = (p^(3*e+3)-1)/(p^3-1) - (p^e-1)/(p-1).
%F A372227 Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = (Pi^2/15) * zeta(3) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 1.03291869994469216597... . (End)
%t A372227 a[n_] := DivisorSum[n, EulerPhi[#] * DivisorSigma[1, #^2] &]; Array[a, 100] (* _Amiram Eldar_, May 20 2024 *)
%o A372227 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*sigma(d^2));
%Y A372227 Cf. A062952, A372998, A373000.
%Y A372227 Cf. A062380, A372996.
%Y A372227 Cf. A005117.
%Y A372227 Cf. A002117, A182448.
%K A372227 nonn,mult
%O A372227 1,2
%A A372227 _Seiichi Manyama_, May 19 2024