OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..386
FORMULA
G.f.: Sum_{k>=1} k^(k-1)*phi(k)*x^k/(1 - (k*x)^k).
a(n) = Sum_{d|n} d^(n-1)*phi(d).
a(n) = Sum_{k=1..n} (n/gcd(n,k))^(n-1).
From Richard L. Ollerton, May 08 2021: (Start)
a(n) = Sum_{k=1..n} phi(gcd(n,k)^n)/phi(n/gcd(n,k)).
a(n) = Sum_{k=1..n} gcd(n,k)^(n-1)*phi(gcd(n,k))/phi(n/gcd(n,k)). (End)
MATHEMATICA
Table[Sum[EulerPhi[d^n], {d, Divisors[n]}], {n, 19}]
nmax = 19; Rest[CoefficientList[Series[Sum[k^(k - 1) EulerPhi[k] x^k/(1 - (k x)^k), {k, 1, nmax}], {x, 0, nmax}], x]]
Table[Sum[(n/GCD[n, k])^(n - 1), {k, n}], {n, 19}]
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d^n)); \\ Michel Marcus, Nov 06 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 06 2018
STATUS
approved