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 A372608 #23 Aug 05 2025 02:58:54
%S A372608 1,3,10,18,44,40,114,124,198,192,430,292,708,540,704,888,1552,954,
%T A372608 2178,1456,1980,2080,3806,2216,4220,3480,4734,4056,7588,3560,9270,
%U A372608 6960,7920,7840,9936,7296,15588,10980,13056,11120,21240,10128,24570,16360,17880,19360,32062
%N A372608 a(n) = Sum_{k=1..n} phi(n*k).
%H A372608 Seiichi Manyama, <a href="/A372608/b372608.txt">Table of n, a(n) for n = 1..10000</a>
%H A372608 Vaclav Kotesovec, <a href="/A372608/a372608.jpg">Graph - the asymptotic ratio (100000 terms)</a>
%H A372608 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F A372608 a(n) = A372606(n,n).
%F A372608 a(n) = A000010(n) * A070639(n).
%F A372608 Sum_{k=1..n} a(k) ~ c * n^4, where c = 3*A065463/(4*Pi^2) = 0.053531188209636805... - _Vaclav Kotesovec_, Aug 04 2025
%t A372608 Table[Sum[EulerPhi[n*k], {k, 1, n}], {n, 1, 50}] (* _Vaclav Kotesovec_, Aug 04 2025 *)
%o A372608 (PARI) a(n) = sum(k=1, n, eulerphi(k*n));
%Y A372608 Main diagonal of A372606.
%Y A372608 Cf. A000010, A070639, A065463.
%K A372608 nonn
%O A372608 1,2
%A A372608 _Seiichi Manyama_, May 07 2024