A342619 a(n) = Sum_{d|n} phi(n/d)^(n-d+1).

1, 2, 9, 18, 1025, 98, 279937, 65666, 10077825, 1310722, 100000000001, 16780802, 106993205379073, 91424858114, 35184439199745, 281476050460674, 295147905179352825857, 118486616186882, 708235345355337676357633, 1152921796664688642, 46005120518729441509377, 11000000000000000000002

Offset: 1

Author

Seiichi Manyama, Mar 16 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A000010, A342612.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#]^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)

PARI

a(n) = sumdiv(n, d, eulerphi(n/d)^(n-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)*x)^k/(1-eulerphi(k)^(k-1)*x^k)))

Formula

a(n) = Sum_{k=1..n} phi(n/gcd(k,n))^(n - gcd(k,n)).

G.f.: Sum_{k>=1} (phi(k) * x)^k/(1 - phi(k)^(k-1) * x^k).

If p is prime, a(p) = 1 + (p-1)^p.