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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

%I

%S 5,6,14,15,21,22,29,30,34,39,78,102,110,138,141,145,190,210,255,291,

%T 330,366,374,395,410,429,434,455,465,546,561,574,609,646,759,791,805,

%U 889,905,915,985,1086,1111,1154,1155,1190,1295,1326,1406,1446,1605,1785,1995

%N 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.

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

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

%H Jinyuan Wang, <a href="/A335785/b335785.txt">Table of n, a(n) for n = 1..671</a> (terms 1..281 from Michel Marcus)

%H Michael A. Bennett, <a href="http://dx.doi.org/10.4064/aa105-4-3">Lucas' square pyramid problem revisited</a>, Acta Arithmetica 105 (2002), 341-347.

%H Michel Marcus and Jinyuan Wang, <a href="/A335715/a335715.txt">PARI program</a>

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

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

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

%K nonn

%O 1,1

%A _Michel Marcus_, Jun 23 2020

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