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

%I A226499 #10 May 05 2021 18:09:18
%S A226499 0,1,6,4851
%N A226499 Triangular numbers representable as m * triangular(m).
%e A226499 6 = 2 * triangular(2).
%e A226499 4851 = 21 * triangular(21).
%t A226499 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 A226499 (Python)
%o A226499 def isTriangular(a):
%o A226499     sr = 1 << (int.bit_length(int(a)) >> 1)
%o A226499     a += a
%o A226499     while a < sr*(sr+1):  sr>>=1
%o A226499     b = sr>>1
%o A226499     while b:
%o A226499       s = sr+b
%o A226499       if a >= s*(s+1):  sr = s
%o A226499       b>>=1
%o A226499     return (a==sr*(sr+1))
%o A226499 for n in range(10000):
%o A226499   product = n*n*(n+1)//2
%o A226499   if isTriangular(product):  print(product, end=',')
%Y A226499 Cf. A000217.
%K A226499 nonn
%O A226499 1,3
%A A226499 _Alex Ratushnyak_, Jun 09 2013