The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297968 Number of solutions to x*y*(x+y)=n in coprime integers. 2
 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)=0 if n is odd. - Robert Israel, Jan 10 2018 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 C. L. Stewart, On the number of solutions of polynomial congruences and Thue equations, J. Amer. Math. Soc. 4 (1991), 793-835. S. Y. Xiao et al, Integers h such that xy(x+y)=h has many integer solutions, Math Overflow EXAMPLE For n=6 the a(n)=6 solutions are (x,y) = (-3,1), (-3,2), (1,-3), (1,2), (2,1) and (2,-3). MAPLE f:= proc(n) local d, count, x, s, ys; d:= numtheory:-divisors(n); count:= 0: for x in d union map(`-`, d) do if issqr(x^4+4*n*x) then s:= sqrt(x^4+4*n*x); ys:= select(t -> type(t, integer) and igcd(t, x)=1, [-(s+x^2)/(2*x), (x^2-s)/(2*x)]); count:= count + nops(ys); fi od; count end proc: map(f, [\$1..200]); MATHEMATICA f[n_] := Module[{d, count, x, s, ys}, d = Divisors[n]; count = 0; Do[If[ IntegerQ[Sqrt[x^4 + 4n x]], s = Sqrt[x^4 + 4n x]; ys = Select[{-(s+x^2)/ (2x), (x^2-s)/(2x)}, IntegerQ[#] && GCD[#, x] == 1&]; count = count + Length[ys]], {x, Union[d, -d]}]; count]; Array[f, 200] (* Jean-François Alcover, Apr 29 2019, after Robert Israel *) CROSSREFS Sequence in context: A284103 A151674 A367631 * A243000 A285214 A285340 Adjacent sequences: A297965 A297966 A297967 * A297969 A297970 A297971 KEYWORD nonn AUTHOR Robert Israel, Jan 10 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 08:45 EDT 2024. Contains 373424 sequences. (Running on oeis4.)