A335785 Squarefree numbers m such that the equation x*(x+1)*(x+2) = m*y^2 has at least one solution (x,y) with x > 0 and y > 0.

5, 6, 14, 15, 21, 22, 29, 30, 34, 39, 78, 102, 110, 138, 141, 145, 190, 210, 255, 291, 330, 366, 374, 395, 410, 429, 434, 455, 465, 546, 561, 574, 609, 646, 759, 791, 805, 889, 905, 915, 985, 1086, 1111, 1154, 1155, 1190, 1295, 1326, 1406, 1446, 1605, 1785, 1995

Offset

1,1

Comments

There are only 2 primes in this sequence, 5 and 29. See Bennett, Corollary 2.3.

There are actually 281 terms up to 10^5 rather than 280 as mentioned in Bennett, who agrees with this.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..671 (terms 1..281 from Michel Marcus)

Michael A. Bennett, Lucas' square pyramid problem revisited, Acta Arithmetica 105 (2002), 341-347.

Michel Marcus and Jinyuan Wang, PARI program.

Example

5 is a term since x*(x+1)*(x+2) = 5*y^2 has 1 solution (x,y) = (8,12).

Crossrefs

Cf. A000330 (square pyramidal numbers), A005117 (squarefree numbers).

Cf. A335715 (more than one solution), A336145.

Sequence in context: A294572 A084381 A289895 * A266304 A359329 A308839

Adjacent sequences: A335782 A335783 A335784 * A335786 A335787 A335788

Keyword

nonn

Author

Michel Marcus, Jun 23 2020

Status

approved