A394787 - OEIS

%I #4 Apr 24 2026 18:39:35

%S 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,

%T 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,

%U 12,10,11,12,12,10,15,11,7,6,10,8,6,12,7,8

%N 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.

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

%t t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - x^2 <= 0, {},

%t        Map[({x, #, Quotient[n - x^2, #]} &),

%t        Select[Divisors[n - x^2], Divisible[n - x^2, #] &]]], {x, 1,

%t        Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];

%t c = ((#1)^2 >= #2*#3 &);

%t Join[{0}, Table[Length[t[n, c]], {n, 1, 130}]]

%t (* _Peter J. C. Moses_, Mar 29 2026 *)

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

%K nonn

%O 0,7

%A _Clark Kimberling_, Apr 19 2026