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 A112886 Triangle-free positive integers. 11
 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 * A282429 A111040 A191324 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 25 14:26 EDT 2019. Contains 326324 sequences. (Running on oeis4.)