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 A342490 #18 Mar 20 2021 11:02:45 %S A342490 1,2,5,10,257,66,46657,16514,1679873,524290,10000000001,4200450, %T A342490 8916100448257,26121388034,4398314962945,35185445863426, %U A342490 18446744073709551617,33853319151618,39346408075296537575425,144115737832194050,3833763648605916233729,2000000000000000000002 %N A342490 a(n) = Sum_{d|n} phi(d)^(n-1). %H A342490 Seiichi Manyama, <a href="/A342490/b342490.txt">Table of n, a(n) for n = 1..388</a> %F A342490 a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(n-2). %F A342490 G.f.: Sum_{k>=1} phi(k)^(k-1) * x^k/(1 - (phi(k) * x)^k). %F A342490 If p is prime, a(p) = 1 + (p-1)^(p-1) = A014566(p-1). %t A342490 a[n_] := DivisorSum[n, EulerPhi[#]^(n-1) &]; Array[a, 20] (* _Amiram Eldar_, Mar 14 2021 *) %o A342490 (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n-1)); %o A342490 (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-2)); %o A342490 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k-1)*x^k/(1-(eulerphi(k)*x)^k))) %Y A342490 Cf. A000010, A014566, A342471, A342487. %K A342490 nonn %O A342490 1,2 %A A342490 _Seiichi Manyama_, Mar 13 2021