A372969 - OEIS

%I #16 May 25 2024 09:01:40

%S 1,7,79,991,15621,277495,5764795,133955071,3486666301,99951163687,

%T 3138428376711,106980008889391,3937376385699277,155563347996105679,

%U 6568408050364922499,295145653362359140351,14063084452067724990993,708233993284902846818911

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

%H Seiichi Manyama, <a href="/A372969/b372969.txt">Table of n, a(n) for n = 1..385</a>

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

%F 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.

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

%Y Main diagonal of A372968.

%Y Cf. A108223.

%K nonn

%O 1,2

%A _Seiichi Manyama_, May 18 2024