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A345688 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 v.

%I A345688 #9 Jun 25 2021 01:53:07
%S A345688 0,3,38,128,550,1028,3254,6128,12600,19624,41432,60111,111656,154860,
%T A345688 224450,318556,517074,662843,1012238,1283975,1683692,2131307,3047040,
%U A345688 3663423,4862454,5934995,7524506,9033407,11960318,13803500,17895182,21162944,25284962,29539043
%N A345688 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 v.
%C A345688 The factor n^4 is to ensure that a(n) is an integer.
%C A345688 A345427(n) = n^2*mu where mu is the mean of the values of v.
%C A345688 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345688 (Python)
%o A345688 from statistics import pvariance
%o A345688 from sympy.core.numbers import igcdex
%o A345688 def A345688(n): return pvariance(n**2*v for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))
%Y A345688 Cf. A345427, A345687.
%K A345688 nonn
%O A345688 1,2
%A A345688 _Chai Wah Wu_, Jun 24 2021