

A345725


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+v and m is the number of such values.


1



0, 0, 10, 28, 166, 224, 964, 1624, 3626, 4934, 12308, 15928, 33670, 42828, 62656, 85016, 154016, 181254, 301688, 364896, 480428, 580134, 901698, 1021274, 1412852, 1655336, 2149650, 2503910, 3518644, 3847556, 5247764, 6093004, 7339188, 8291404, 10135408, 11018524
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OFFSET

1,3


COMMENTS

The factor m^2 is to ensure that a(n) is an integer.
A345425(n) = m*mu where mu is the mean of the values of u+v.
The population standard deviation sqrt(s) appears to grow linearly with n.


LINKS



PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



