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

1,5

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

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 *)

Crossrefs

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

Sequence in context: A158974 A355659 A152993 * A343379 A026927 A240863

Adjacent sequences: A178130 A178131 A178132 * A178134 A178135 A178136

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 20 2010

Status

approved