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 A342420 #9 Mar 11 2021 17:32:21
%S A342420 1,5,55,517,12501,93371,4941259,67109381,2324522989,40000012505,
%T A342420 2853116706111,35664401886907,3634501279107037,66672040958289359,
%U A342420 3503151123046887555,147573952589743522309,13235844190181388226833,236078448451781550068849,35611553801885644604231623
%N A342420 a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n)).
%F A342420 a(n) = Sum_{d|n} phi(d^(d+1)) = Sum_{d|n} phi(d) * d^d.
%F A342420 G.f.: Sum_{k>=1} phi(k^(k+1))*x^k/(1 - x^k).
%t A342420 a[n_] := Sum[(n/GCD[k, n])^(n/GCD[k, n]), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Mar 11 2021 *)
%o A342420 (PARI) a(n) = sum(k=1, n, (n/gcd(k, n))^(n/gcd(k, n)));
%o A342420 (PARI) a(n) = sumdiv(n, d, eulerphi(d^(d+1)));
%o A342420 (PARI) a(n) = sumdiv(n, d, eulerphi(d)*d^d);
%o A342420 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k^(k+1))*x^k/(1-x^k)))
%Y A342420 Cf. A000010, A226459, A342411.
%K A342420 nonn
%O A342420 1,2
%A A342420 _Seiichi Manyama_, Mar 11 2021