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 A140114 #14 Mar 15 2023 10:50:09
%S A140114 0,0,1,3,2,4,3,5,4,8,5,8,7,6,13,7,7,13,10,12,9,14,14,15,11,12,18,16,
%T A140114 16,17,18,15,16,20,20,21,22,21,18,19,21,24,24,23,25,23,29,21,23,31,29,
%U A140114 23,21,30,33,35,34,27,30,28,29,32,30,31,36,36,36,36,36,43,24,40,38,40,39
%N A140114 Number of semiprimes strictly between n^2 and (n+1)^2.
%C A140114 Can it be proved that a(n)>0 for n>1?
%C A140114 Chen proves that there is a semiprime between n^2 and (n+1)^2 for sufficiently large n. - _T. D. Noe_, Oct 17 2008
%D A140114 Jing Run Chen, On the distribution of almost primes in an interval, Sci. Sinica 18 (1975), 611-627.
%H A140114 T. D. Noe, <a href="/A140114/b140114.txt">Table of n, a(n) for n = 0..1000</a>
%e A140114 The first semiprimes are 6,10,14,15,21,22,26. None are <4, hence a(0)=a(1)=0.
%e A140114 One only is < 9, hence a(2) = 1.
%e A140114 Three more, 10, 14, 15 are < 16, hence a(3)=3.
%t A140114 SemiPrimeQ[n_] := TrueQ[Plus@@Last/@FactorInteger[n]==2]; Table[Length[Select[Range[n^2+1, n^2+2n], SemiPrimeQ]], {n,0,100}] (* _T. D. Noe_, Sep 25 2008 *)
%t A140114 Module[{nn=80,sps},sps=Table[If[PrimeOmega[n]==2,1,0],{n,(nn+1)^2}];Table[ Total[ Take[sps,{k^2+1,(k+1)^2-1}]],{k,0,nn}]] (* _Harvey P. Dale_, Oct 03 2022 *)
%o A140114 (PARI) a(n)=sum(k=n^2+1,n^2+2*n, bigomega(k)==2) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A140114 Cf. A014085.
%K A140114 nonn
%O A140114 0,4
%A A140114 Philippe Lallouet (philip.lallouet(AT)orange.fr), May 08 2008
%E A140114 Corrected, edited and extended by _T. D. Noe_, Sep 25 2008