cp's OEIS Frontend

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.

A205728 Number of odd, nonsquare semiprimes <= n^2.

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%I A205728 #15 Mar 24 2021 15:35:58
%S A205728 0,0,0,1,2,4,5,8,11,16,19,24,28,32,41,46,50,60,66,73,81,89,100,110,
%T A205728 118,126,140,151,163,174,187,197,210,224,239,253,269,286,298,312,326,
%U A205728 344,363,380,399,414,435,451,468,491,513,530,546,567,591,619,643,664
%N A205728 Number of odd, nonsquare semiprimes <= n^2.
%C A205728 Like A205727 (see comments thereto), this looks at odd semiprimes, but excludes squares.  This then relates to the Goldbach conjecture 2j=p+q with the additional restriction that j, p, and q are not equal.
%H A205728 N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
%t A205728 SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; nn = 100;  t = Select[Range[1, nn^2, 2], SemiPrimeQ[#] && ! IntegerQ[Sqrt[#]] &]; Table[Length[Select[t, # <= n^2 &]], {n, nn}] (* _T. D. Noe_, Jan 30 2012 *)
%Y A205728 Cf. A205726, A205727.
%K A205728 nonn
%O A205728 1,5
%A A205728 _Keith Backman_, Jan 30 2012