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A345689 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 A345689 #7 Jun 25 2021 01:59:26
%S A345689 0,3,20,64,236,432,1372,2652,5588,8384,18576,28143,52588,71476,106700,
%T A345689 152688,251698,323451,496672,639599,847700,1059379,1526548,1855287,
%U A345689 2479604,2990859,3827060,4631431,6138690,7153524,9258556,10957212,13153070,15219123,18354306
%N A345689 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 A345689 The factor n^4 is to ensure that a(n) is an integer.
%C A345689 A345432(n) = n^2*mu where mu is the mean of the values of |u|.
%C A345689 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345689 (Python)
%o A345689 from statistics import pvariance
%o A345689 from sympy.core.numbers import igcdex
%o A345689 def A345689(n): return pvariance(n**2*abs(u) for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))
%Y A345689 Cf. A345432, A345687, A345688.
%K A345689 nonn
%O A345689 1,2
%A A345689 _Chai Wah Wu_, Jun 24 2021