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 A209310 Triangular numbers whose sum of triangular divisors is also triangular and greater than 1. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 22 04:01 EDT 2023. Contains 365503 sequences. (Running on oeis4.)