A345687 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, 32, 112, 500, 944, 3072, 5872, 12168, 19004, 40552, 59031, 109992, 152872, 221900, 315420, 513266, 658163, 1006272, 1277375, 1675544, 2121979, 3036460, 3652047, 4848004, 5918355, 7505768, 9012071, 11937118, 13778600, 17866848, 21132736, 25249454, 29499603

Offset: 1

Author

Chai Wah Wu, Jun 23 2021

Keywords

• nonn

Comments

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

A345426(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. A345426.

Programs

Python

from statistics import pvariance
from sympy.core.numbers import igcdex
def A345687(n): return pvariance(n**2*u for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))