A345429 -id:A345429 - cp's OEIS frontend

A345694 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = ux+vy 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

Chai Wah Wu, Jun 24 2021

nonn

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.

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

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)

cp's OEIS Frontend

A345694 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = ux+vy 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.

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cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Crossrefs

Programs

Python

A345694 For 1<=x<=n, 1<=y<=n with gcd(x,y)=1, write 1 = gcd(x,y) = ux+vy 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.