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A226499 Triangular numbers representable as m * triangular(m). 3
0, 1, 6, 4851 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)