cp's OEIS Frontend

A345434 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = sum of the values of u^2+v^2.

%I A345434 #10 Jun 25 2021 00:31:19
%S A345434 1,4,11,20,47,62,135,196,313,394,685,838,1317,1578,1991,2484,3573,
%T A345434 4084,5595,6410,7621,8792,11505,12710,15539,17536,20619,23018,28417,
%U A345434 30650,37215,41308,46405,51072,57607,61596,72927,79670,88055,94618,109799,116312,134067,143952,155287
%N A345434 For 1<=x<=n, 1<=y<=n, write gcd(x,y) = u*x+v*y with u,v minimal; a(n) = sum of the values of u^2+v^2.
%C A345434 Minimal means minimize u^2+v^2. We follow Maple, PARI, etc., in setting u=0 and v=1 when x=y.
%o A345434 (Python)
%o A345434 from sympy.core.numbers import igcdex
%o A345434 def A345434(n): return sum(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))) # _Chai Wah Wu_, Jun 22 2021
%Y A345434 Cf. A345415-A345433.
%K A345434 nonn
%O A345434 1,2
%A A345434 _N. J. A. Sloane_, Jun 22 2021