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A209309
Numbers whose sum of triangular divisors is also triangular and greater than 1.
3
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
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jan 18 2013
STATUS
approved