OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..605
FORMULA
a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n - n/gcd(k,n)).
G.f.: Sum_{k>=1} phi(k) * x^k/(1 - (phi(k) * x)^k).
If p is prime, a(p) = p.
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#]^(n - # + 1) &]; Array[a, 30] (* Amiram Eldar, Mar 17 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n-d+1));
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-n/gcd(k, n)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-(eulerphi(k)*x)^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 16 2021
STATUS
approved