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

1,2

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.

Links

Table of n, a(n) for n=1..34.

Prog

(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)))

Crossrefs

Cf. A345426.

Sequence in context: A197524 A107465 A319219 * A211224 A213845 A221464

Adjacent sequences: A345684 A345685 A345686 * A345688 A345689 A345690

Keyword

nonn

Author

Chai Wah Wu, Jun 23 2021

Status

approved