A342488 a(n) = Sum_{d|n} phi(d)^(n/d+1).

1, 2, 5, 6, 17, 14, 37, 26, 53, 82, 101, 74, 145, 254, 385, 162, 257, 398, 325, 1218, 1697, 1102, 485, 1058, 4497, 1874, 2645, 8394, 785, 19330, 901, 2306, 14497, 4354, 112769, 17738, 1297, 6158, 37697, 270082, 1601, 316130, 1765, 105498, 1165441, 11134, 2117, 162050, 1681381

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..8299

Formula

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

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

If p is prime, a(p) = 1 + (p-1)^2 = A002522(p-1).

a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n) + 1)/phi(n/gcd(k, n)). - Richard L. Ollerton, May 07 2021

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#]^(n/#+1) &]; Array[a, 50] (* Amiram Eldar, Mar 14 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))^gcd(k, n));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^2*x^k/(1-eulerphi(k)*x^k)))

Crossrefs

Cf. A000010, A002522, A164941, A309369, A342485, A342487.

Sequence in context: A306885 A029939 A082198 * A098871 A227623 A146477

Adjacent sequences: A342485 A342486 A342487 * A342489 A342490 A342491

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2021

Status

approved