

A275234


Number of distinct positive solutions to the system of n Diophantine equations: x_1+y_1=x_2*y_2, x_2+y_2=x_3*y_3, ..., x_n+y_n=x_1*y_1.


1



1, 2, 2, 3, 3, 5, 4, 7, 7, 12, 12, 21, 22, 37, 47, 72, 93, 145, 198, 303, 427, 637, 917, 1383, 2008
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OFFSET

1,2


COMMENTS

In any solution, interchanging x_i and y_i for any i yields a new solution. So does a circular permutation of the solution. Two solutions are counted as distinct if one cannot be gotten from the other by these transformations.


LINKS

Table of n, a(n) for n=1..25.
Christopher Briggs, Python script for generating nth term
Christopher Briggs, Y. Hirano, H. Tsutsui, Positive Solutions to Some Systems of Diophantine Equations, Journal of Integer Sequences, 2016 Vol 19 #16.8.4.


EXAMPLE

For n = 1, the only positive solution to x+y = xy is x = y = 2.
For n = 2, the only distinct (see comments) positive solutions to x_1+y_2 = x_2*y_2, x_2+y_2 = x_1+y_1 are (x_1,y_1,x_2,y_2) = (2,2,2,2) or (1,5,2,3).


CROSSREFS

Sequence in context: A035574 A036819 A114328 * A097366 A139807 A308465
Adjacent sequences: A275231 A275232 A275233 * A275235 A275236 A275237


KEYWORD

nonn,more


AUTHOR

Christopher Briggs, Jul 20 2016


STATUS

approved



