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A112886 Triangle-free positive integers. 11

%I

%S 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,

%T 44,46,47,49,52,53,58,59,61,62,64,65,67,68,71,73,74,76,77,79,82,83,85,

%U 86,88,89,92,94,95,97,98,101,103,104,106,107,109,113,115,116,118,119

%N Triangle-free positive integers.

%C Those positive integers not in A113502.

%C a(n) = A132895(n)/2. - _Ray Chandler_, May 29 2008

%H Charles R Greathouse IV, <a href="/A112886/b112886.txt">Table of n, a(n) for n = 1..10000</a>

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

%t v={};Do[If[b=Select[Divisors[n], #>1 && IntegerQ[(1+8#)^(1/2)]&]; b=={}, AppendTo[v, n]], {n, 138}]; v (Firoozbakht)

%t 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 *)

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

%Y Cf. A113502, A000217, A005117.

%K nonn

%O 1,2

%A _Leroy Quet_, Jan 10 2006

%E More terms from _Farideh Firoozbakht_, Jan 12 2006

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Last modified September 16 06:38 EDT 2019. Contains 327090 sequences. (Running on oeis4.)