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A112886 Triangle-free 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 (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

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

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Last modified August 27 12:58 EDT 2016. Contains 275906 sequences.