A342620 a(n) = Sum_{d|n} phi(n/d)^(n+d+1).

1, 2, 33, 66, 16385, 770, 10077697, 1050626, 362805249, 83886082, 10000000000001, 268664834, 15407021574586369, 19747769352194, 2252074693689345, 18014673389486082, 75557863725914323419137, 25593109118189570, 229468251895129407139872769, 73788172563556335618, 6624765697237267477692417, 11000000000000000000000002

Offset

1,2

Links

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

Formula

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

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

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

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#]^(n + # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)^(n+d+1));
(PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n+gcd(k, n)));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+2)*x^k/(1-eulerphi(k)^(k+1)*x^k)))

Crossrefs

Cf. A000010, A342613.

Sequence in context: A116340 A003347 A303375 * A065647 A041127 A282726

Adjacent sequences: A342617 A342618 A342619 * A342621 A342622 A342623

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved