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

0, 0, 0, 1, 2, 4, 5, 8, 11, 16, 19, 24, 28, 32, 41, 46, 50, 60, 66, 73, 81, 89, 100, 110, 118, 126, 140, 151, 163, 174, 187, 197, 210, 224, 239, 253, 269, 286, 298, 312, 326, 344, 363, 380, 399, 414, 435, 451, 468, 491, 513, 530, 546, 567, 591, 619, 643, 664

Offset: 1

Author

Keith Backman, Jan 30 2012

Keywords

• nonn

Comments

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.

Links

• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Crossrefs

Cf. A205726, A205727.

Programs

Mathematica

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 *)