A209309 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

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 *)

PROG

(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)))}