A372969 a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} n/gcd(x_1, x_2, ... , x_n, n).

1, 7, 79, 991, 15621, 277495, 5764795, 133955071, 3486666301, 99951163687, 3138428376711, 106980008889391, 3937376385699277, 155563347996105679, 6568408050364922499, 295145653362359140351, 14063084452067724990993, 708233993284902846818911

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..385

Formula

a(n) = Sum_{d|n} mu(n/d) * n/d * sigma_{n+1}(d).

a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} ( gcd(x_1, x_2, ... , x_{n-1}, n)/gcd(x_1, x_2, ... , x_n, n) )^n.

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*n/d*sigma(d, n+1));

Crossrefs

Main diagonal of A372968.

Cf. A108223.

Sequence in context: A127890 A198973 A127859 * A014293 A176792 A186377

Adjacent sequences: A372966 A372967 A372968 * A372970 A372971 A372972

Keyword

nonn

Author

Seiichi Manyama, May 18 2024

Status

approved