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A342471
a(n) = Sum_{d|n} phi(d)^n.
7
1, 2, 9, 18, 1025, 130, 279937, 65794, 10078209, 2097154, 100000000001, 16789506, 106993205379073, 156728328194, 35185445863425, 281479271743490, 295147905179352825857, 203119913861122, 708235345355337676357633, 1152923703631151106
OFFSET
1,2
FORMULA
a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(n-1).
G.f.: Sum_{k>=1} (phi(k)*x)^k/(1 - (phi(k)*x)^k).
If p is prime, a(p) = 1 + (p-1)^p = A110567(p-1).
a(n) = Sum_{k=1..n} phi(gcd(n,k))^n/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#]^n &]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)^n);
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-1));
(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 13 2021
STATUS
approved