A345688 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, 38, 128, 550, 1028, 3254, 6128, 12600, 19624, 41432, 60111, 111656, 154860, 224450, 318556, 517074, 662843, 1012238, 1283975, 1683692, 2131307, 3047040, 3663423, 4862454, 5934995, 7524506, 9033407, 11960318, 13803500, 17895182, 21162944, 25284962, 29539043

Offset

1,2

Comments

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

A345427(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.

Links

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

Prog

(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345688(n): return pvariance(n**2*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. A345427, A345687.

Sequence in context: A241895 A093939 A129122 * A002405 A050394 A281798

Adjacent sequences: A345685 A345686 A345687 * A345689 A345690 A345691

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved