A345689 - OEIS

%I #7 Jun 25 2021 01:59:26

%S 0,3,20,64,236,432,1372,2652,5588,8384,18576,28143,52588,71476,106700,

%T 152688,251698,323451,496672,639599,847700,1059379,1526548,1855287,

%U 2479604,2990859,3827060,4631431,6138690,7153524,9258556,10957212,13153070,15219123,18354306

%N 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 The factor n^4 is to ensure that a(n) is an integer.

%C A345432(n) = n^2*mu where mu is the mean of the values of |u|.

%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 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 Cf. A345432, A345687, A345688.

%K nonn

%O 1,2

%A _Chai Wah Wu_, Jun 24 2021