A342607 a(n) = Sum_{d|n} phi(d)^(n-d).

1, 2, 2, 3, 2, 11, 2, 19, 66, 1027, 2, 835, 2, 279939, 1052674, 69635, 2, 10114563, 2, 1074855939, 78364426242, 100000000003, 2, 4315152387, 1099511627778, 106993205379075, 101559973445634, 21937029021319171, 2, 1162183941554179, 2, 562950221856771, 10000000000001073741826

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) - 1).

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

If p is prime, a(p) = 2.

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A164941, A342608, A342612, A342628.

Sequence in context: A162733 A016003 A087139 * A226422 A375765 A016005

Adjacent sequences: A342604 A342605 A342606 * A342608 A342609 A342610

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved