A345691 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^2+v^2.

0, 0, 14, 48, 1266, 1988, 21514, 49392, 171032, 242964, 882708, 1487996, 3650020, 4913620, 9374594, 14382448, 29859148, 38410016, 71427550, 97525500, 147544988, 186821472, 320133640, 399015644, 605818854, 740618592, 1061345430, 1349418108, 2017326672, 2390222900

Offset

1,3

Comments

The factor n^4 is to ensure that a(n) is an integer.

A345434(n) = n^2*mu where mu is the mean of the values of u^2+v^2.

s^(1/4) appears to grow linearly with n.

Links

Table of n, a(n) for n=1..30.

Prog

(Python)
from statistics import pvariance
from sympy.core.numbers import igcdex
def A345691(n): return pvariance(n**2*(u**2+v**2) for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)))

Crossrefs

Cf. A345434, A345687, A345688, A345689, A345690.

Sequence in context: A337421 A345724 A121202 * A251228 A250973 A039340

Adjacent sequences: A345688 A345689 A345690 * A345692 A345693 A345694

Keyword

nonn

Author

Chai Wah Wu, Jun 24 2021

Status

approved