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

1,2

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

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 *)

Crossrefs

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

Sequence in context: A032984 A108379 A348256 * A108378 A084588 A309548

Adjacent sequences: A082654 A082655 A082656 * A082658 A082659 A082660

Keyword

nonn

Author

Jason Earls, May 17 2003

Status

approved