

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, 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
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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 A174239 A066249
Adjacent sequences: A276502 A276503 A276504 * A276506 A276507 A276508


KEYWORD

easy,nonn


AUTHOR

Dmitry Badziahin, Sep 12 2016


STATUS

approved



