A342542 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n) - 1).

1, 2, 3, 4, 5, 7, 7, 9, 15, 13, 11, 33, 13, 19, 105, 33, 17, 91, 19, 209, 469, 31, 23, 641, 1045, 37, 1627, 841, 29, 4217, 31, 673, 10461, 49, 29785, 10281, 37, 55, 49465, 68769, 41, 65197, 43, 12281, 529625, 67, 47, 273185, 279979, 1049661, 1049121, 52657, 53, 803647

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..5000

Formula

a(n) = Sum_{d|n} phi(n/d) * phi(d)^(n/d-1).

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

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#-1) &]; Array[a, 50] (* Amiram Eldar, Mar 15 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(n/gcd(k, n)-1));
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(n/d-1));

Crossrefs

Cf. A000010, A029935, A342473, A342540, A342541, A342544.

Sequence in context: A325353 A117174 A320466 * A338671 A343246 A348531

Adjacent sequences: A342539 A342540 A342541 * A342543 A342544 A342545

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2021

Status

approved