cp's OEIS Frontend

A345430 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) = sum of the values of |v|.

%I A345430 #10 Jun 25 2021 00:32:06
%S A345430 1,2,5,8,17,20,38,50,71,83,128,146,209,236,278,326,434,473,608,668,
%T A345430 758,833,1031,1103,1292,1400,1583,1709,2024,2120,2480,2672,2912,3104,
%U A345430 3410,3572,4085,4328,4670,4910,5540,5738,6431,6761,7163,7526,8354,8642,9416,9788,10388
%N A345430 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) = sum of the values of |v|.
%C A345430 Minimal means minimize u^2+v^2. We follow Maple, PARI, etc., in setting u=0 and v=1 when x=y.
%o A345430 (Python)
%o A345430 from sympy.core.numbers import igcdex
%o A345430 def A345430(n): return sum(abs(v) for u, v, w in (igcdex(x,y) for x in range(1,n+1) for y in range(1,n+1)) if w == 1) # _Chai Wah Wu_, Jun 22 2021
%Y A345430 Cf. A345415-A345434.
%K A345430 nonn
%O A345430 1,2
%A A345430 _N. J. A. Sloane_, Jun 22 2021