A345693 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 v and m is the number of such values.

0, 2, 26, 72, 374, 516, 2064, 3634, 7706, 10472, 25832, 34298, 70946, 90106, 128664, 177428, 317024, 376150, 623276, 757856, 987038, 1189074, 1829210, 2094022, 2885790, 3380040, 4348400, 5089782, 7135460, 7836276, 10701330, 12423438, 14837870, 16813314, 20405200

Offset

1,2

Comments

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

A345424(n) = m*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..35.

Prog

(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345693(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)*v for u, v, w in zlist)

Crossrefs

Cf. A345423, A345687, A345688, A345689, A345690, A345691, A345692.

Sequence in context: A210848 A247957 A152997 * A229573 A337396 A067204

Adjacent sequences: A345690 A345691 A345692 * A345694 A345695 A345696

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved