A082657 Integers expressible as the sum of a square and a triangular number in just one way.

1, 2, 3, 4, 5, 6, 11, 12, 14, 16, 17, 21, 24, 25, 29, 30, 32, 35, 36, 39, 42, 44, 49, 50, 51, 53, 54, 56, 57, 65, 66, 71, 72, 74, 75, 77, 78, 80, 81, 84, 95, 96, 101, 104, 105, 107, 110, 116, 117, 119, 120, 122, 126, 128, 129, 131, 137, 141, 149, 150, 152, 153, 156, 161

Offset: 1

Author

Jason Earls, May 17 2003

Keywords

• nonn

Comments

It is assumed here that 0 is a square but not a triangular number. - Amiram Eldar, Dec 08 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A000290, A082658, A082659, A082660.

Programs

Mathematica

aQ[n_] := Length @ Solve[x^2 + y (y + 1)/2 == n && x >= 0 && y > 0, {x, y}, Integers] == 1; Select[Range[161], aQ] (* Amiram Eldar, Dec 08 2019 *)