A276505 - OEIS

A276505

Number of rational numbers > 1 whose numerator in reduced form equals n and that can be written as a continued fraction with exactly three partial quotients.

%I #19 Oct 05 2016 10:28:41

%S 0,0,1,1,3,1,5,2,5,3,7,2,9,3,6,6,11,1,11,4,9,7,11,4,13,5,9,6,15,3,17,

%T 6,10,7,12,6,19,7,9,7,19,4,17,8,11,11,17,3,21,5,14,10,17,5,19,11,17,9,

%U 17,4,21,9,10,12,21,7,23,8,16,7,25,7,25,7,7,14

%N Number of rational numbers > 1 whose numerator in reduced form equals n and that can be written as a continued fraction with exactly three partial quotients.

%C Equivalently, this is the number of solutions of the equation n = xyz + x + z in positive integer x, y and z.

%e For n=5 there are three rational numbers which satisfy all the conditions: 5/2 = [2;1,1], 5/3 = [1;1,2] and 5/4 = [1;3,1]. Therefore a(5) = 3.

%K easy,nonn

%O 1,5

%A _Dmitry Badziahin_, Sep 12 2016