A209311 Numbers whose sum of triangular divisors is also a divisor and greater than 1.

285, 1302, 1425, 1820, 2508, 3640, 3720, 4845, 4956, 5016, 5415, 7125, 7280, 9100, 9114, 9912, 11685, 12255, 12740, 14508, 15105, 16815, 17385, 18200, 19095, 19824, 20235, 20805, 22134, 22515, 23655, 23660, 24021, 24738, 25365, 25480, 27075, 27588, 27645

Offset

1,1

Links

Antonio Roldán, Table of n, a(n) for n = 1..13202 (terms < 10^7)

Example

285 is in the sequence because its divisors being 1, 3, 5, 15, 19, 57, 95, 285, of which 1, 3 and 15 are triangular, these add up to 19.
1302 is in sequence because the sum of triangular divisors 21 + 6 + 3 + 1 = 31 is divisor of 1302.

Mathematica

TriangularQ[n_] := IntegerQ[Sqrt[1 + 8*n]]; fQ[n_] := Module[{tri = Total[Select[Divisors[n], TriangularQ]]}, tri > 1 && Mod[n, tri] == 0]; Select[Range[28000], fQ] (* T. D. Noe, Jan 23 2013 *)

Prog

(PARI) istriangular(n)=issquare(8*n+1)
{t=0; for(n=1, 10^7, k=sumdiv(n, d, istriangular(d)*d); if(n/k==n\k&&k>>1, t+=1; write("b209311.txt", t, " ", n)))}

Crossrefs

Cf. A185027, A035316, A209309, A209310.

Sequence in context: A043415 A288037 A105921 * A176712 A225881 A332919

Adjacent sequences: A209308 A209309 A209310 * A209312 A209313 A209314

Keyword

nonn

Author

Antonio Roldán, Jan 18 2013

Status

approved