A342473 a(n) = Sum_{d|n} phi(d)^d.

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

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) - 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)))

Crossrefs

Cf. A000010, A029939, A110567, A309369, A338997, A342470, A342471, A342485.

Sequence in context: A109298 A297470 A075537 * A342619 A342471 A180852

Adjacent sequences: A342470 A342471 A342472 * A342474 A342475 A342476

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2021

Status

approved