A345692 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = m^2*s, where s is the population variance of the values of u and m is the number of such values.

0, 2, 24, 68, 364, 504, 2040, 3606, 7664, 10422, 25764, 34226, 70836, 89994, 128532, 177276, 316844, 375952, 623024, 757604, 986742, 1188760, 1828860, 2093672, 2885342, 3379568, 4347890, 5089220, 7134860, 7835684, 10700654, 12422758, 14837078, 16812466, 20404320

Offset

1,2

Comments

The factor m^2 is to ensure that a(n) is an integer.

A345423(n) = m*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..35.

Prog

(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345692(n):
    zlist = [z for z in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)) if z[2] == 1]
    return pvariance(len(zlist)*u for u, v, w in zlist)

Crossrefs

Cf. A345423, A345687, A345688, A345689, A345690, A345691.

Sequence in context: A068878 A100918 A152965 * A139284 A003614 A195189

Adjacent sequences: A345689 A345690 A345691 * A345693 A345694 A345695

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved