A226499 - OEIS

%I #10 May 05 2021 18:09:18

%S 0,1,6,4851

%N Triangular numbers representable as m * triangular(m).

%e 6 = 2 * triangular(2).

%e 4851 = 21 * triangular(21).

%t 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 *)

%o (Python)

%o def isTriangular(a):

%o     sr = 1 << (int.bit_length(int(a)) >> 1)

%o     a += a

%o     while a < sr*(sr+1):  sr>>=1

%o     b = sr>>1

%o     while b:

%o       s = sr+b

%o       if a >= s*(s+1):  sr = s

%o       b>>=1

%o     return (a==sr*(sr+1))

%o for n in range(10000):

%o   product = n*n*(n+1)//2

%o   if isTriangular(product):  print(product, end=',')

%Y Cf. A000217.

%K nonn

%O 1,3

%A _Alex Ratushnyak_, Jun 09 2013