A342617 a(n) = Sum_{d|n} phi(d)^(n-d+1).

1, 2, 3, 4, 5, 20, 7, 38, 135, 4102, 11, 1670, 13, 1679624, 4202505, 270346, 17, 60539912, 19, 4299292682, 470185508877, 1000000000012, 23, 17253793802, 4398046511125, 1283918464548878, 609359773564947, 131622174060806158, 29, 4789472952582154, 31

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..605

Formula

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

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

If p is prime, a(p) = p.

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#]^(n - # + 1) &]; Array[a, 30] (* Amiram Eldar, Mar 17 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n-d+1));
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n-n/gcd(k, n)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)*x^k/(1-(eulerphi(k)*x)^k)))

Crossrefs

Cf. A000010, A342607.

Sequence in context: A261639 A333993 A362064 * A329579 A024635 A217679

Adjacent sequences: A342614 A342615 A342616 * A342618 A342619 A342620

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved