cp's OEIS Frontend

A345690 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 |v|.

%I A345690 #7 Jun 25 2021 01:59:23
%S A345690 0,3,14,48,166,324,1078,2172,4760,7204,16508,25479,48376,66016,99650,
%T A345690 143600,238914,308115,476038,615239,818300,1024179,1481652,1804167,
%U A345690 2417654,2918787,3742442,4535391,6022574,7025184,9105478,10784796,12958370,15000299,18108116
%N A345690 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 |v|.
%C A345690 The factor n^4 is to ensure that a(n) is an integer.
%C A345690 A345433(n) = n^2*mu where mu is the mean of the values of |v|.
%C A345690 The population standard deviation sqrt(s) appears to grow linearly with n.
%o A345690 (Python)
%o A345690 from statistics import pvariance
%o A345690 from sympy.core.numbers import igcdex
%o A345690 def A345690(n): return pvariance(n**2*abs(v) for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)))
%Y A345690 Cf. A345433, A345687, A345688, A345689.
%K A345690 nonn
%O A345690 1,2
%A A345690 _Chai Wah Wu_, Jun 24 2021