A342370 a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).

1, 3, 11, 68, 629, 7797, 117655, 2097254, 43046979, 1000000799, 25937424611, 743008402000, 23298085122493, 793714773374529, 29192926027528343, 1152921504613147242, 48661191875666868497, 2185911559739107208115, 104127350297911241532859, 5242880000000008181608132

Offset: 1

Author

Seiichi Manyama, Mar 13 2021

Keywords

• nonn

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A000010, A018804, A056665, A173235, A341036, A342394, A342433, A342436, A342449.

Programs

Mathematica

a[n_] := Sum[GCD[k, n]^(k - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)

PARI

a(n) = sum(k=1, n, gcd(k, n)^(k-1));

Formula

If p is prime, a(p) = p-1 + p^(p-1) = A173235(p).

Extensions

a(19) and beyond from Martin Ehrenstein, Mar 13 2021