A345690 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 |v|.

0, 3, 14, 48, 166, 324, 1078, 2172, 4760, 7204, 16508, 25479, 48376, 66016, 99650, 143600, 238914, 308115, 476038, 615239, 818300, 1024179, 1481652, 1804167, 2417654, 2918787, 3742442, 4535391, 6022574, 7025184, 9105478, 10784796, 12958370, 15000299, 18108116

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.

A345433(n) = n^2*mu where mu is the mean of the values of |v|.

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

Crossrefs

Cf. A345433, A345687, A345688, A345689.

Programs

Python

from statistics import pvariance
from sympy.core.numbers import igcdex
def A345690(n): return pvariance(n**2*abs(v) for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))