A335715 Squarefree numbers m such that the equation x*(x+1)*(x+2) = m*y^2 has more than one solution (x,y) with x>0 and y>0.

6, 210, 546, 915, 1785, 7230, 13395, 16206, 17490, 20930, 76245, 104006, 228486, 508530, 563766

Offset

1,1

Comments

7453355, 9147666, 19073886, 61622814, 648402306, 22023958326, 748181603526 are also terms. - Jinyuan Wang, Jul 28 2020

Links

Table of n, a(n) for n=1..15.

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

Michel Marcus and Jinyuan Wang, PARI program

Example

6 is a term since x*(x+1)*(x+2) = 6*y^2 has 3 positive integer solutions : (1,1), (2,2) and (48,140) that give (1,1) and (24,70) for s*(s+1)*(2s+1) = 6*t^2 with a (x=2s, y=2t) variable change (see A000330 where A000330(n) = n*(n+1)*(2*n+1)/6).

Crossrefs

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

Cf. A335785 (at least one solution), A336145.

Sequence in context: A136742 A334285 A068969 * A094805 A055193 A346015

Adjacent sequences: A335712 A335713 A335714 * A335716 A335717 A335718

Keyword

nonn,more

Author

Michel Marcus, Jun 18 2020

Extensions

a(12) from Michel Marcus, Jun 24 2020

a(13)-a(15) from Jinyuan Wang, Jul 28 2020

Status

approved