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A178133
Number of odd semiprimes between consecutive squares.
2
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved