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A345694 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = m^2*s, where s is the population variance of the values of |u| and m is the number of such values.

%I A345694 #8 Jun 25 2021 01:53:28
%S A345694 0,2,12,28,124,168,696,1254,2800,3734,9684,13282,27576,34818,51828,
%T A345694 71660,129380,153172,254624,312716,413774,496600,767976,879284,
%U A345694 1219286,1422992,1845842,2173556,3043292,3345884,4556174,5288806,6365966,7188082,8786288,9615066
%N A345694 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = m^2*s, where s is the population variance of the values of |u| and m is the number of such values.
%C A345694 The factor m^2 is to ensure that a(n) is an integer.
%C A345694 A345429(n) = m*mu where mu is the mean of the values of |u|.
%C A345694 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345694 (Python)
%o A345694 from statistics import pvariance
%o A345694 from sympy.core.numbers import igcdex
%o A345694 def A345694(n):
%o A345694     zlist = [z for z in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)) if z[2] == 1]
%o A345694     return pvariance(len(zlist)*abs(u) for u, v, w in zlist)
%Y A345694 Cf. A345429, A345687, A345688, A345689, A345690, A345691, A345692, A345693.
%K A345694 nonn
%O A345694 1,2
%A A345694 _Chai Wah Wu_, Jun 24 2021