A097571 Numbers n such that triangular number t(n) (see A000217) = n(n+1)/2 is a product of three consecutive integers.

0, 3, 15, 20, 44, 608, 22736

Offset: 1

Author

N. J. A. Sloane, Aug 29 2004

Keywords

• nonn
• fini
• full

Comments

Replacing "three" by "two" we get A001652.

Replacing "three" by "N" we get: {15} for N = 4 and 5, {2079} for N = 6 and no solutions for N >= 7. - J. B. M. Melissen.

t(a(n)) equals x*(x+1)*(x+2) for x = [0, 1, 4, 5, 9, 56, 636]n. - _Zak Seidov, Jun 21 2013

Links

• S. P. Mohanty, Which triangular numbers are products of three consecutive integers?, Acta Mathematica Hungarica 1991, Volume 58, Issue 1-2, pp 31-36.

Crossrefs

Cf. A000217, A001219, A001652.

Programs

Mathematica

(Sqrt[8#+1]-1)/2&/@Select[Table[n(n+1)(n+2),{n,0,23000}],OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Jan 12 2023 *)