A227054 a(n) = least triangular number t > 0 such that n*t is a triangular number, or 0 if no such t exists.

1, 3, 1, 0, 3, 1, 3, 15, 0, 1, 6, 3, 6, 15, 1, 0, 78, 21, 10, 6, 1, 3, 45, 190, 0, 3, 55, 1, 15, 10, 15, 28203, 45, 105, 3, 1, 465, 120, 55, 3, 21, 15, 21, 3570, 1, 6, 210, 861, 0, 6, 3, 15, 105, 21945, 1, 21, 3, 66, 26565, 91, 276, 378, 6, 0, 1596, 1, 300

Offset: 1

Author

Alex Ratushnyak, Jun 29 2013

Keywords

• nonn

Comments

a(n) = 1 if and only if n is a triangular number.

Indices of conjectured 0's: 4, 9, 16, 25, 49, 64, 81, 121, 144, 169, 225, 256, 289, 361, 400, 441, 529, 576, 625, 729, ... These are squares of 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27.

a(n) = 0 if n = p^(2*j) where p is a prime and j > 0. - Jon E. Schoenfield, Sep 17 2023

Examples

			a(614) = 13964154294535688630985 = A000217(167117648945) because 614 * a(614) = A000217(4141012131555), and none of the smaller triangular numbers t satisfies 614*t = A000217(m) for some m.
		

Crossrefs

Cf. A166478 (indices of t in A000217), A225502, A225503.

Extensions

a(1)-a(25) and a(49)-a(67) from Jon E. Schoenfield, Sep 17 2023