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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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 mentionned 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 A308839 A099330

Adjacent sequences:  A335782 A335783 A335784 * A335786 A335787 A335788

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 23 2020

STATUS

approved

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Last modified July 3 14:21 EDT 2022. Contains 355055 sequences. (Running on oeis4.)