A345694 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, 12, 28, 124, 168, 696, 1254, 2800, 3734, 9684, 13282, 27576, 34818, 51828, 71660, 129380, 153172, 254624, 312716, 413774, 496600, 767976, 879284, 1219286, 1422992, 1845842, 2173556, 3043292, 3345884, 4556174, 5288806, 6365966, 7188082, 8786288, 9615066

Offset

1,2

Comments

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

A345429(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..36.

Prog

(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345694(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)*abs(u) for u, v, w in zlist)

Crossrefs

Cf. A345429, A345687, A345688, A345689, A345690, A345691, A345692, A345693.

Sequence in context: A211623 A034318 A338798 * A326517 A248119 A240764

Adjacent sequences: A345691 A345692 A345693 * A345695 A345696 A345697

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved