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

1,1

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)))}

Crossrefs

Cf. A000217, A035316, A185027, A209310.

Sequence in context: A031478 A073455 A279894 * A020333 A044831 A033003

Adjacent sequences: A209306 A209307 A209308 * A209310 A209311 A209312

Keyword

nonn

Author

Antonio Roldán, Jan 18 2013

Status

approved