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A342473
a(n) = Sum_{d|n} phi(d)^d.
5
1, 2, 9, 18, 1025, 74, 279937, 65554, 10077705, 1049602, 100000000001, 16777306, 106993205379073, 78364444034, 35184372089865, 281474976776210, 295147905179352825857, 101559966746186, 708235345355337676357633, 1152921504607896594, 46005119909369701746057, 10000000000100000000002
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(n/gcd(k, n) - 1).
G.f.: Sum_{k>=1} (phi(k) * x)^k/(1 - 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))^gcd(n,k)/phi(n/gcd(n,k)). - Richard L. Ollerton, May 07 2021
MATHEMATICA
a[n_] := DivisorSum[n, EulerPhi[#]^# &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(d)^d);
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n/gcd(k, n)-1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)*x)^k/(1-x^k)))
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 13 2021
STATUS
approved