This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112886 #37 Jun 07 2025 22:25:04
%S A112886 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 A112886 44,46,47,49,52,53,58,59,61,62,64,65,67,68,71,73,74,76,77,79,82,83,85,
%U A112886 86,88,89,92,94,95,97,98,101,103,104,106,107,109,113,115,116,118,119
%N A112886 Positive integers that have no triangular divisors > 1.
%C A112886 Sequence consists of those positive integers not in A113502.
%C A112886 (Pi^(3/2))/density is empirically close to 10. - _Richard Peterson_, Apr 06 2025
%H A112886 Charles R Greathouse IV, <a href="/A112886/b112886.txt">Table of n, a(n) for n = 1..10000</a>
%F A112886 a(n) = A132895(n)/2. - _Ray Chandler_, May 29 2008
%e A112886 14 is included because the divisors of 14 are 1, 2, 7 and 14, none of which are triangular numbers > 1.
%t A112886 v={};Do[If[b=Select[Divisors[n], #>1 && IntegerQ[(1+8#)^(1/2)]&]; b=={}, AppendTo[v, n]], {n, 138}]; v (Firoozbakht)
%t A112886 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 A112886 (PARI) is(n)=fordiv(n, d, if(ispolygonal(d, 3) && d>1, return(0))); 1 \\ _Charles R Greathouse IV_, Jul 31 2016
%o A112886 (Python)
%o A112886 from itertools import count, islice
%o A112886 from sympy import divisors
%o A112886 from sympy.ntheory.primetest import is_square
%o A112886 def A112886_gen(startvalue=1): # generator of terms >= startvalue
%o A112886 return filter(lambda n:all(d==1 or not is_square((d<<3)+1) for d in divisors(n,generator=True)), count(max(startvalue,1)))
%o A112886 A112886_list = list(islice(A112886_gen(),40)) # _Chai Wah Wu_, Jun 07 2025
%Y A112886 Cf. A113502, A000217, A005117, A132895.
%K A112886 nonn
%O A112886 1,2
%A A112886 _Leroy Quet_, Jan 10 2006
%E A112886 More terms from _Farideh Firoozbakht_, Jan 12 2006
%E A112886 Name edited (based on a suggestion from _Michel Marcus_) by _Jon E. Schoenfield_, Jul 02 2021