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 A342607 #23 Mar 19 2021 07:00:54 %S A342607 1,2,2,3,2,11,2,19,66,1027,2,835,2,279939,1052674,69635,2,10114563,2, %T A342607 1074855939,78364426242,100000000003,2,4315152387,1099511627778, %U A342607 106993205379075,101559973445634,21937029021319171,2,1162183941554179,2,562950221856771,10000000000001073741826 %N A342607 a(n) = Sum_{d|n} phi(d)^(n-d). %H A342607 Seiichi Manyama, <a href="/A342607/b342607.txt">Table of n, a(n) for n = 1..605</a> %F A342607 a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n - n/gcd(k,n) - 1). %F A342607 G.f.: Sum_{k>=1} x^k/(1 - (phi(k) * x)^k). %F A342607 If p is prime, a(p) = 2. %t A342607 a[n_] := DivisorSum[n, EulerPhi[#]^(n - #) &]; Array[a, 30] (* _Amiram Eldar_, Mar 17 2021 *) %o A342607 (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n-d)); %o A342607 (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-n/gcd(k, n)-1)); %o A342607 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(eulerphi(k)*x)^k))) %Y A342607 Cf. A000010, A164941, A342608, A342612, A342628. %K A342607 nonn %O A342607 1,2 %A A342607 _Seiichi Manyama_, Mar 16 2021