A345689 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|.

0, 3, 20, 64, 236, 432, 1372, 2652, 5588, 8384, 18576, 28143, 52588, 71476, 106700, 152688, 251698, 323451, 496672, 639599, 847700, 1059379, 1526548, 1855287, 2479604, 2990859, 3827060, 4631431, 6138690, 7153524, 9258556, 10957212, 13153070, 15219123, 18354306

Offset: 1

Author

Chai Wah Wu, Jun 24 2021

Keywords

• nonn

Comments

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

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

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

Crossrefs

Cf. A345432, A345687, A345688.

Programs

Python

from statistics import pvariance
from sympy.core.numbers import igcdex
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)))