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.

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.

Links

Table of n, a(n) for n=1..36.

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)

Crossrefs

Cf. A345430, A345687, A345688, A345689, A345690, A345691, A345692, A345693, A345694.

Sequence in context: A119062 A270822 A248117 * A336958 A305600 A058373

Adjacent sequences: A345692 A345693 A345694 * A345696 A345697 A345698

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved