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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

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

PROG

(Python)

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)

CROSSREFS

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

Sequence in context: A211623 A034318 A338798 * A326517 A248119 A240764

Adjacent sequences:  A345691 A345692 A345693 * A345695 A345696 A345697

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Jun 24 2021

STATUS

approved

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Last modified May 21 05:37 EDT 2022. Contains 353889 sequences. (Running on oeis4.)