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.

0, 0, 14, 48, 250, 452, 1578, 2816, 6120, 9556, 20220, 28476, 54596, 75092, 111050, 155120, 253852, 323792, 497054, 624700, 828476, 1049584, 1510824, 1792476, 2397166, 2924432, 3736358, 4469884, 5919800, 6804500, 8811122, 10401536, 12541844, 14621072, 17574850

Offset

1,3

Comments

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

A345428(n) = n^2*mu where mu is the mean of the values of u+v.

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

Links

Table of n, a(n) for n=1..35.

Prog

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

Crossrefs

Cf. A345428, A345687, A345688, A345689, A345690, A345691.

Sequence in context: A205468 A195966 A337421 * A121202 A345691 A251228

Adjacent sequences: A345721 A345722 A345723 * A345725 A345726 A345727

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved