cp's OEIS Frontend

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.

%I A345695 #8 Jun 25 2021 01:59:19
%S A345695 0,2,10,24,110,152,656,1198,2714,3632,9512,13082,27274,34474,51416,
%T A345695 71168,128704,152430,253648,311636,412538,495234,766258,877438,
%U A345695 1217102,1420616,1843136,2170622,3039784,3342200,4551830,5284110,6360830,7182594,8780236,9608714
%N 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.
%C A345695 The factor m^2 is to ensure that a(n) is an integer.
%C A345695 A345430(n) = m*mu where mu is the mean of the values of |v|.
%C A345695 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345695 (Python)
%o A345695 from statistics import pvariance
%o A345695 from sympy.core.numbers import igcdex
%o A345695 def A345695(n):
%o A345695     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]
%o A345695     return pvariance(len(zlist)*abs(v) for u, v, w in zlist)
%Y A345695 Cf. A345430, A345687, A345688, A345689, A345690, A345691, A345692, A345693, A345694.
%K A345695 nonn
%O A345695 1,2
%A A345695 _Chai Wah Wu_, Jun 24 2021