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 A309369 #15 Mar 13 2021 10:52:16
%S A309369 1,2,3,4,5,8,7,10,15,22,11,34,13,44,105,42,17,116,19,314,357,112,23,
%T A309369 426,1045,158,747,1474,29,5290,31,594,3069,274,24185,6082,37,344,9945,
%U A309369 67922,41,63542,43,12170,303225,508,47,74834,279979,1050022,135201,29098,53,309872,4294345
%N A309369 a(n) = Sum_{d|n} phi(n/d)^d, where phi = Euler totient function (A000010).
%H A309369 Seiichi Manyama, <a href="/A309369/b309369.txt">Table of n, a(n) for n = 1..5000</a>
%F A309369 G.f.: Sum_{k>=1} phi(k)*x^k/(1 - phi(k)*x^k).
%F A309369 L.g.f.: -log(Product_{k>=1} (1 - phi(k)*x^k)^(1/k)).
%F A309369 a(p) = p for p prime.
%F A309369 a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(gcd(k, n) - 1). - _Seiichi Manyama_, Mar 13 2021
%t A309369 Table[Sum[EulerPhi[n/d]^d, {d, Divisors[n]}], {n, 1, 55}]
%t A309369 nmax = 55; CoefficientList[Series[Sum[EulerPhi[k] x^k/(1 - EulerPhi[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A309369 nmax = 55; CoefficientList[Series[-Log[Product[(1 - EulerPhi[k] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest
%o A309369 (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(gcd(k, n)-1)); \\ _Seiichi Manyama_, Mar 13 2021
%Y A309369 Cf. A000010, A055225, A164941, A264782, A279789.
%K A309369 nonn
%O A309369 1,2
%A A309369 _Ilya Gutkovskiy_, Jul 25 2019