A342541 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n)).

1, 2, 4, 5, 8, 10, 12, 14, 28, 28, 20, 62, 24, 54, 272, 68, 32, 198, 36, 676, 1224, 130, 44, 1348, 4136, 180, 3540, 3426, 56, 12632, 60, 1640, 22520, 304, 129456, 22370, 72, 378, 101808, 270952, 80, 192996, 84, 40630, 1867184, 550, 92, 551528, 1679700, 4198860, 2105408

Offset: 1

Author

Seiichi Manyama, Mar 15 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A029935, A342485, A342539, A342542, A342543.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#) &]; Array[a, 50] (* Amiram Eldar, Mar 15 2021 *)

PARI

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

PARI

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

Formula

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

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