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.

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

Offset

1,5

Comments

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

Links

Table of n, a(n) for n=1..76.

Example

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.

Crossrefs

Sequence in context: A094367 A092368 A225080 * A201901 A331381 A174239

Adjacent sequences: A276502 A276503 A276504 * A276506 A276507 A276508

Keyword

easy,nonn

Author

Dmitry Badziahin, Sep 12 2016

Status

approved