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

2

`%I #15 Mar 24 2021 15:35:58
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`%S 0,0,0,1,2,4,5,8,11,16,19,24,28,32,41,46,50,60,66,73,81,89,100,110,
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`%T 118,126,140,151,163,174,187,197,210,224,239,253,269,286,298,312,326,
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`%U 344,363,380,399,414,435,451,468,491,513,530,546,567,591,619,643,664
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`%N Number of odd, nonsquare semiprimes <= n^2.
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`%C 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.
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`%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)
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`%t 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 *)
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`%Y Cf. A205726, A205727.
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`%K nonn
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`%O 1,5
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`%A _Keith Backman_, Jan 30 2012
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