A209309 Numbers whose sum of triangular divisors is also triangular and greater than 1.

6, 12, 18, 24, 48, 54, 96, 102, 110, 114, 138, 162, 174, 186, 192, 204, 220, 222, 228, 246, 258, 282, 315, 318, 348, 354, 364, 366, 372, 384, 402, 414, 426, 438, 440, 444, 456, 474, 486, 492, 498, 516, 522, 534, 550, 558, 564, 582, 606, 618, 636, 642, 654, 678

Offset: 1

Author

Antonio Roldán, Jan 18 2013

Keywords

• nonn

Examples

			186 is a term because the sum of its triangular divisors, 1+3+6 = 10 is also triangular.
		

Links

• Antonio Roldán, Table of n, a(n) for n = 1..8055 (terms <= 10^5)

Crossrefs

Cf. A000217, A035316, A185027, A209310.

Programs

Mathematica

triQ[n_] := n > 1 && IntegerQ[Sqrt[8*n+1]]; q[n_] := triQ[1 + DivisorSum[n, #&, triQ[#] &]]; Select[Range[700], q] (* Amiram Eldar, Aug 12 2023 *)

PARI

istriangular(n)=issquare(8*n+1)
{t=0; for(n=1, 10^5, k=sumdiv(n, d, istriangular(d)*d); if(istriangular(k)&&k>>1, t+=1; write("b209309.txt",t," ",n)))}