A342539 a(n) = Sum_{k=1..n} phi(gcd(k, n))^n.

1, 2, 10, 19, 1028, 132, 279942, 65798, 10078726, 2097160, 100000000010, 16797702, 106993205379084, 156728328204, 35186519703560, 281479271809036, 295147905179352825872, 203119914385420, 708235345355337676357650, 1152924803145924620, 46005163783270994804748, 20000000000000000000020

Offset: 1

Author

Seiichi Manyama, Mar 15 2021

Keywords

• nonn

Links

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

Crossrefs

Cf. A000010, A029935, A332517, A342487, A342534, A342535, A342540, A342541, A342543.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^n &]; Array[a, 20] (* Amiram Eldar, Mar 15 2021 *)

PARI

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

PARI

a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^n);

Formula

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

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

a(n) = Sum_{k=1..n} phi(n/gcd(n,k))^(n-1)*phi(gcd(n,k)). - Richard L. Ollerton, May 09 2021