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A345695
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.
3
0, 2, 10, 24, 110, 152, 656, 1198, 2714, 3632, 9512, 13082, 27274, 34474, 51416, 71168, 128704, 152430, 253648, 311636, 412538, 495234, 766258, 877438, 1217102, 1420616, 1843136, 2170622, 3039784, 3342200, 4551830, 5284110, 6360830, 7182594, 8780236, 9608714
OFFSET
1,2
COMMENTS
The factor m^2 is to ensure that a(n) is an integer.
A345430(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.
PROG
(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345695(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(v) for u, v, w in zlist)
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jun 24 2021
STATUS
approved