A395636 a(n) = number of triples (x, y, z) such that 2*x^2 + y*z = n, where x, y, z are distinct primes satisfying y < z.

1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 2, 2, 0, 0, 1, 2

Offset

23,34

Links

Table of n, a(n) for n=23..108.

Example

a(23) = 1 counts this triple: (2,3,5).
a(56) = 2 counts these triples: (3,2,19), (5,2,3).

Mathematica

t[n_, c_] := Module[{r}, r = Flatten[Table[If[n - 2 x^2 <= 0, {},
Map[({x, #, Quotient[n - 2 x^2, #]} &),
Select[Divisors[n - 2 x^2], Divisible[n - 2 x^2, #] &]]],
{x, 1, Floor[Sqrt[n - 1]]}], 1]; Select[r, Apply[c, #] &]];
c = (PrimeQ[#1] && PrimeQ[#2] && PrimeQ[#3] && #2 < #3 &&
     DuplicateFreeQ[{#1, #2, #3}] &);
Table[Length[t[n, c]], {n, 23, 130}]
(* Peter J. C. Moses, Mar 29 2026 *)

Crossrefs

Cf. A393710, A394038, A394788, A395634, A395637.

Sequence in context: A109527 A373241 A362424 * A186715 A331983 A219485

Adjacent sequences: A395633 A395634 A395635 * A395637 A395638 A395639

Keyword

nonn

Author

Clark Kimberling, May 09 2026

Status

approved