A209310 Triangular numbers whose sum of triangular divisors is also triangular and greater than 1.

6, 4186, 32131, 52975, 78210, 111628, 237016, 247456, 584821, 750925, 1464616, 3649051, 5791906, 11297881, 16082956, 24650731, 27243271, 38618866, 46585378, 51546781, 56026405, 76923406, 89880528, 96070591, 126906346, 164629585, 201854278, 228733966

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

Example

4186 is in sequence because it is triangular (4186 = 91*92/2) and the sum of its triangular divisors, 4186+91+1 = 4278 is also triangular (4278 = 92*93/2).

Mathematica

triQ[n_] := n > 1 && IntegerQ[Sqrt[8*n+1]]; q[n_] := triQ[1 + DivisorSum[n, #&, triQ[#] &]]; Select[Accumulate[Range[22000]], q] (* Amiram Eldar, Aug 12 2023 *)

Prog

(PARI) istriangular(n)=issquare(8*n+1)
{t=0; for(n=1, 10^8, if(istriangular(n), k=sumdiv(n, d, istriangular(d)*d) ; if(istriangular(k)&&k>>1, t+=1; write("b209310.txt", t, " ", n))))}

Crossrefs

Subsequence of A209309.

Cf. A000217, A185027, A035316.

Sequence in context: A024087 A161845 A317485 * A268504 A099723 A226499

Adjacent sequences: A209307 A209308 A209309 * A209311 A209312 A209313

Keyword

nonn

Author

Antonio Roldán, Jan 18 2013

Status

approved