A394787 a(n) = number of triples (x, y, z) such that x^2 + y*z = n, where x,y,z are positive integers satisfying x^2 >= y*z.

0, 0, 1, 0, 0, 1, 2, 2, 3, 0, 1, 2, 2, 3, 2, 4, 2, 5, 5, 2, 3, 2, 4, 2, 4, 3, 5, 4, 8, 5, 6, 8, 7, 4, 3, 4, 2, 7, 4, 6, 7, 7, 6, 8, 6, 9, 8, 6, 8, 10, 8, 6, 7, 5, 8, 6, 8, 8, 7, 6, 10, 9, 6, 8, 10, 8, 12, 10, 11, 12, 12, 10, 15, 11, 7, 6, 10, 8, 6, 12, 7, 8

Offset

0,7

Links

Table of n, a(n) for n=0..81.

Example

a(17) = 5 counts these triples: (3, 1, 8), (3, 2, 4), (3, 4, 2), (3, 8, 1), (4, 1, 1).

Mathematica

t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - x^2 <= 0, {},
       Map[({x, #, Quotient[n - x^2, #]} &),
       Select[Divisors[n - x^2], Divisible[n - x^2, #] &]]], {x, 1,
       Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];
c = ((#1)^2 >= #2*#3 &);
Join[{0}, Table[Length[t[n, c]], {n, 1, 130}]]
(* Peter J. C. Moses, Mar 29 2026 *)

Crossrefs

Cf. A393710, A394740, A394743, A394785, A394788.

Sequence in context: A139365 A071479 A257398 * A182631 A231728 A303545

Adjacent sequences: A394784 A394785 A394786 * A394788 A394789 A394790

Keyword

nonn

Author

Clark Kimberling, Apr 19 2026

Status

approved