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

%I A372969 #16 May 25 2024 09:01:40
%S A372969 1,7,79,991,15621,277495,5764795,133955071,3486666301,99951163687,
%T A372969 3138428376711,106980008889391,3937376385699277,155563347996105679,
%U A372969 6568408050364922499,295145653362359140351,14063084452067724990993,708233993284902846818911
%N A372969 a(n) = Sum_{1 <= x_1, x_2, ... , x_n <= n} n/gcd(x_1, x_2, ... , x_n, n).
%H A372969 Seiichi Manyama, <a href="/A372969/b372969.txt">Table of n, a(n) for n = 1..385</a>
%F A372969 a(n) = Sum_{d|n} mu(n/d) * n/d * sigma_{n+1}(d).
%F A372969 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 A372969 (PARI) a(n) = sumdiv(n, d, moebius(n/d)*n/d*sigma(d, n+1));
%Y A372969 Main diagonal of A372968.
%Y A372969 Cf. A108223.
%K A372969 nonn
%O A372969 1,2
%A A372969 _Seiichi Manyama_, May 18 2024