

A112886


Trianglefree positive integers.


10



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
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OFFSET

1,2


COMMENTS

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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


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 *)


PROG

(PARI) is(n)=fordiv(n, d, if(ispolygonal(d, 3) && d>1, return(0))); 1 \\ Charles R Greathouse IV, Jul 31 2016


CROSSREFS

Cf. A113502, A000217, A005117.
Sequence in context: A206285 A229303 A262978 * 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



