A342618 a(n) = Sum_{d|n} phi(d)^(n+d+1).

1, 2, 129, 514, 4194305, 9218, 470184984577, 17179877378, 609359740018689, 4402341478402, 100000000000000000000001, 1125899907563522, 137370551967459378662586974209, 36845784908492735250434, 9903520314283046597240029185

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..220

Formula

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

G.f.: Sum_{k>=1} phi(k)^(2*k+1) * x^k/(1 - (phi(k) * x)^k).

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

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#]^(n + # + 1) &]; Array[a, 15] (* 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=20, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(2*k+1)*x^k/(1-(eulerphi(k)*x)^k)))

Crossrefs

Cf. A000010, A342608.

Sequence in context: A090121 A003369 A303377 * A258806 A216358 A361890

Adjacent sequences: A342615 A342616 A342617 * A342619 A342620 A342621

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved