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 A342487 #17 Mar 20 2021 11:02:18 %S A342487 1,2,17,34,4097,258,1679617,262658,60467201,8388610,1000000000001, %T A342487 67133442,1283918464548865,940369969154,281479271743489, %U A342487 2251816993685506,4722366482869645213697,1218719481069570,12748236216396078174437377,9223380832949895170 %N A342487 a(n) = Sum_{d|n} phi(d)^(n+1). %H A342487 Seiichi Manyama, <a href="/A342487/b342487.txt">Table of n, a(n) for n = 1..388</a> %F A342487 a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^n. %F A342487 G.f.: Sum_{k>=1} phi(k)^(k+1) * x^k/(1 - (phi(k) * x)^k). %F A342487 If p is prime, a(p) = 1 + (p-1)^(p+1). %t A342487 a[n_] := DivisorSum[n, EulerPhi[#]^(n+1) &]; Array[a, 20] (* _Amiram Eldar_, Mar 14 2021 *) %o A342487 (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n+1)); %o A342487 (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^n); %o A342487 (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 A342487 Cf. A000010, A342471, A342485, A342488, A342490. %K A342487 nonn %O A342487 1,2 %A A342487 _Seiichi Manyama_, Mar 13 2021