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A345687 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = n^4*s, where s is the population variance of the values of u. 12
0, 3, 32, 112, 500, 944, 3072, 5872, 12168, 19004, 40552, 59031, 109992, 152872, 221900, 315420, 513266, 658163, 1006272, 1277375, 1675544, 2121979, 3036460, 3652047, 4848004, 5918355, 7505768, 9012071, 11937118, 13778600, 17866848, 21132736, 25249454, 29499603 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The factor n^4 is to ensure that a(n) is an integer.
A345426(n) = n^2*mu where mu is the mean of the values of u.
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
def A345687(n): return pvariance(n**2*u for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)))
CROSSREFS
Cf. A345426.
Sequence in context: A197524 A107465 A319219 * A211224 A213845 A221464
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jun 23 2021
STATUS
approved

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Last modified February 22 04:44 EST 2024. Contains 370239 sequences. (Running on oeis4.)