A178133 Number of odd semiprimes between consecutive squares.

0, 0, 1, 1, 2, 1, 3, 3, 5, 3, 5, 4, 4, 9, 5, 4, 10, 6, 7, 8, 8, 11, 10, 8, 8, 14, 11, 12, 11, 13, 10, 13, 14, 15, 14, 16, 17, 12, 14, 14, 18, 19, 17, 19, 15, 21, 16, 17, 23, 22, 17, 16, 21, 24, 28, 24, 21, 23, 20, 24, 22, 24, 21, 27, 28, 28, 26, 28, 32, 19, 31, 29, 27, 29, 28, 22, 37

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 20 2010

Keywords

• nonn

Comments

Odd squarefree semiprimes: 15, 21, 33, 35, 39, 51, 55, 57, 65, 69, 77, 85, 87, 91, 93, 95, 111,.... Between 1^2 and 2^2 there are no odd squarefree semiprimes, between 2^2 and 3^2 there are no odd squarefree semiprimes, between 3^2 and 4^2 there is one odd squarefree semiprime 15, between 4^2 and 5^2 there is one odd squarefree semiprimes 21, between 5^2 and 6^2 there are two odd squarefree semiprimes 33,35.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A140114 (number of semiprimes between squares), A046388, A188443.

Programs

Mathematica

fQ[n_] := OddQ[n] && Last /@ FactorInteger[n] == {1, 1}; f[n_] := Length[Select[ Range[n^2, (n + 1)^2], fQ]]; Array[f, 77] (* Robert G. Wilson v, Jun 07 2011 *)