A342608 a(n) = Sum_{d|n} phi(d)^(n+d).

1, 2, 65, 258, 1048577, 4610, 78364164097, 4294971394, 101559956672513, 1100585369602, 10000000000000000000001, 281474977071106, 11447545997288281555215581185, 6140964151415455875074, 1237940039285381374411014145, 79228162514264619068521709570

Offset: 1

Author

Seiichi Manyama, Mar 16 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..220

Crossrefs

Cf. A000010, A342488, A342607, A342613.

Programs

Mathematica

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

PARI

a(n) = sumdiv(n, d, eulerphi(d)^(n+d));

PARI

a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n+n/gcd(k, n)-1));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (eulerphi(k)^2*x)^k/(1-(eulerphi(k)*x)^k)))

Formula

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

G.f.: Sum_{k>=1} (phi(k)^2 * x)^k/(1 - (phi(k) * x)^k).

If p is prime, a(p) = 1 + (p-1)^(2*p).