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
Keywords
Examples
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).
Links
- Donovan Johnson, Table of n, a(n) for n = 1..1000
Programs
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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 *)
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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))))}