cp's OEIS Frontend

A345724 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+v.

%I A345724 #10 Jun 25 2021 01:59:12
%S A345724 0,0,14,48,250,452,1578,2816,6120,9556,20220,28476,54596,75092,111050,
%T A345724 155120,253852,323792,497054,624700,828476,1049584,1510824,1792476,
%U A345724 2397166,2924432,3736358,4469884,5919800,6804500,8811122,10401536,12541844,14621072,17574850
%N A345724 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+v.
%C A345724 The factor n^4 is to ensure that a(n) is an integer.
%C A345724 A345428(n) = n^2*mu where mu is the mean of the values of u+v.
%C A345724 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345724 (Python)
%o A345724 from statistics import pvariance
%o A345724 from sympy.core.numbers import igcdex
%o A345724 def A345724(n): return pvariance(n**2*(u+v) for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))
%Y A345724 Cf. A345428, A345687, A345688, A345689, A345690, A345691.
%K A345724 nonn
%O A345724 1,3
%A A345724 _Chai Wah Wu_, Jun 24 2021