A342543 a(n) = Sum_{k=1..n} phi(gcd(k, n))^gcd(k, n).

1, 2, 10, 19, 1028, 76, 279942, 65558, 10077718, 1049608, 100000000010, 16777334, 106993205379084, 78364444044, 35184372090920, 281474976776236, 295147905179352825872, 101559966746268, 708235345355337676357650, 1152921504607897676, 46005119909369702026044, 10000000000100000000020

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, A342423, A342488, A342539, A342541, A342544.

Programs

Mathematica

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

PARI

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

PARI

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

Formula

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

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