A226499 Triangular numbers representable as m * triangular(m).

0, 1, 6, 4851

Offset

1,3

Links

Table of n, a(n) for n=1..4.

Example

6 = 2 * triangular(2).
4851 = 21 * triangular(21).

Mathematica

TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; s = Select[Range[0, 10000], TriangularQ[#^2 (# + 1)/2] &]; s^2 (s + 1)/2 (* T. D. Noe, Jun 12 2013 *)

Prog

(Python)
def isTriangular(a):
    sr = 1 << (int.bit_length(int(a)) >> 1)
    a += a
    while a < sr*(sr+1):  sr>>=1
    b = sr>>1
    while b:
      s = sr+b
      if a >= s*(s+1):  sr = s
      b>>=1
    return (a==sr*(sr+1))
for n in range(10000):
  product = n*n*(n+1)//2
  if isTriangular(product):  print(product, end=', ')

Crossrefs

Cf. A000217.

Sequence in context: A209310 A268504 A099723 * A343096 A066061 A028366

Adjacent sequences: A226496 A226497 A226498 * A226500 A226501 A226502

Keyword

nonn

Author

Alex Ratushnyak, Jun 09 2013

Status

approved