A342544 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(gcd(k, n) - 1).

1, 2, 6, 11, 260, 40, 46662, 16398, 1679630, 262408, 10000000010, 4194366, 8916100448268, 13060740684, 4398046511640, 35184372105244, 18446744073709551632, 16926661124436, 39346408075296537575442, 144115188076118572, 3833759992447475215524, 1000000000010000000020

Offset

1,2

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(# - 1) &]; Array[a, 20] (* Amiram Eldar, Mar 15 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(gcd(k, n)-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(d-1));

Crossrefs

Cf. A000010, A029935, A309369, A342436, A342540, A342542, A342543.

Sequence in context: A368810 A208893 A057294 * A342540 A328449 A293589

Adjacent sequences: A342541 A342542 A342543 * A342545 A342546 A342547

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2021

Status

approved