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A345687 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = n^4*s, where s is the population variance of the values of u.

%I A345687 #10 Jun 25 2021 01:53:35
%S A345687 0,3,32,112,500,944,3072,5872,12168,19004,40552,59031,109992,152872,
%T A345687 221900,315420,513266,658163,1006272,1277375,1675544,2121979,3036460,
%U A345687 3652047,4848004,5918355,7505768,9012071,11937118,13778600,17866848,21132736,25249454,29499603
%N A345687 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = n^4*s, where s is the population variance of the values of u.
%C A345687 The factor n^4 is to ensure that a(n) is an integer.
%C A345687 A345426(n) = n^2*mu where mu is the mean of the values of u.
%C A345687 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345687 (Python)
%o A345687 from statistics import pvariance
%o A345687 from sympy.core.numbers import igcdex
%o A345687 def A345687(n): return pvariance(n**2*u for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))
%Y A345687 Cf. A345426.
%K A345687 nonn
%O A345687 1,2
%A A345687 _Chai Wah Wu_, Jun 23 2021