

A112886


Trianglefree positive integers.


9



1, 2, 4, 5, 7, 8, 11, 13, 14, 16, 17, 19, 22, 23, 25, 26, 29, 31, 32, 34, 35, 37, 38, 41, 43, 44, 46, 47, 49, 52, 53, 58, 59, 61, 62, 64, 65, 67, 68, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 88, 89, 92, 94, 95, 97, 98, 101, 103, 104, 106, 107, 109, 113, 115, 116, 118, 119
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Those positive integers not in A113502.
a(n) = A132895(n)/2.  Ray Chandler, May 29 2008


LINKS

Table of n, a(n) for n=1..67.


EXAMPLE

14 is included because the divisors of 14 are 1, 2, 7 and 14, none of which are triangular numbers > 1.


MATHEMATICA

v={}; Do[If[b=Select[Divisors[n], #>1 && IntegerQ[(1+8#)^(1/2)]&]; b=={}, AppendTo[v, n]], {n, 138}]; v (Firoozbakht)
tfpnQ[n_]:=Module[{nn=120, trnos}, trnos=Rest[Accumulate[ Range[ (Sqrt[8nn+1]1)/2+1]]]; Intersection[ Divisors[ n], trnos]=={}]; Select[Range[ 120], tfpnQ] (* Harvey P. Dale, Jul 17 2015 *)


CROSSREFS

Cf. A113502, A000217, A005117.
Sequence in context: A188298 A206285 A229303 * A111040 A191324 A147807
Adjacent sequences: A112883 A112884 A112885 * A112887 A112888 A112889


KEYWORD

nonn


AUTHOR

Leroy Quet, Jan 10 2006


EXTENSIONS

More terms from Farideh Firoozbakht, Jan 12 2006


STATUS

approved



