A345693 - OEIS

%I #12 Jul 29 2023 06:44:54

%S 0,2,26,72,374,516,2064,3634,7706,10472,25832,34298,70946,90106,

%T 128664,177428,317024,376150,623276,757856,987038,1189074,1829210,

%U 2094022,2885790,3380040,4348400,5089782,7135460,7836276,10701330,12423438,14837870,16813314,20405200

%N 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 v and m is the number of such values.

%C The factor m^2 is to ensure that a(n) is an integer.

%C A345424(n) = m*mu where mu is the mean of the values of v.

%C The population standard deviation sqrt(s) appears to grow linearly with n.

%o (Python)

%o from statistics import pvariance

%o from sympy.core.numbers import igcdex

%o def A345693(n):

%o     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     return pvariance(len(zlist)*v for u, v, w in zlist)

%Y Cf. A345423, A345687, A345688, A345689, A345690, A345691, A345692.

%K nonn

%O 1,2

%A _Chai Wah Wu_, Jun 24 2021