VOOZH about

URL: https://oeis.org/A209311

⇱ A209311 - OEIS

login
A209311
Numbers whose sum of triangular divisors is also a divisor and greater than 1.
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
KEYWORD
nonn
AUTHOR
Antonio Roldán, Jan 18 2013
STATUS
approved