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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 (list; graph; refs; listen; history; text; internal format)
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 A278629

Adjacent sequences:  A209308 A209309 A209310 * A209312 A209313 A209314

KEYWORD

nonn

AUTHOR

Antonio Roldán, Jan 18 2013

STATUS

approved

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Last modified September 16 08:36 EDT 2019. Contains 327091 sequences. (Running on oeis4.)