OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..388
FORMULA
a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(n/gcd(k, n)).
G.f.: Sum_{k>=1} phi(k)^(k+1) * x^k/(1 - x^k).
If p is prime, a(p) = 1 + (p-1)^(p+1).
a(n) = Sum_{k=1..n} phi(gcd(n,k))^(gcd(n,k) + 1)/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#]^(#+1) &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)^(d+1));
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n/gcd(k, n)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+1)*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 13 2021
STATUS
approved