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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.
6
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.
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
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jun 24 2021
STATUS
approved