

A140114


Number of semiprimes strictly between n^2 and (n+1)^2.


3



0, 0, 1, 3, 2, 4, 3, 5, 4, 8, 5, 8, 7, 6, 13, 7, 7, 13, 10, 12, 9, 14, 14, 15, 11, 12, 18, 16, 16, 17, 18, 15, 16, 20, 20, 21, 22, 21, 18, 19, 21, 24, 24, 23, 25, 23, 29, 21, 23, 31, 29, 23, 21, 30, 33, 35, 34, 27, 30, 28, 29, 32, 30, 31, 36, 36, 36, 36, 36, 43, 24, 40, 38, 40, 39
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OFFSET

0,4


COMMENTS

Can it be proved that a(n)>0 for n>1?
Chen proves that there is a semiprime between n^2 and (n+1)^2 for sufficiently large n.  T. D. Noe, Oct 17 2008


REFERENCES

Jing Run Chen, On the distribution of almost primes in an interval, Sci. Sinica 18 (1975), 611627.


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000


EXAMPLE

The first semiprimes are 6,10,14,15,21,22,26. None are <4, hence a(0)=a(1)=0.
One only is < 9, hence a(2) = 1.
Three more, 10, 14, 15 are < 16, hence a(3)=3.


MATHEMATICA

SemiPrimeQ[n_] := TrueQ[Plus@@Last/@FactorInteger[n]==2]; Table[Length[Select[Range[n^2+1, n^2+2n], SemiPrimeQ]], {n, 0, 100}]  T. D. Noe, Sep 25 2008


PROG

(PARI) a(n)=sum(k=n^2+1, n^2+2*n, bigomega(k)==2) \\ Charles R Greathouse IV, Jan 31 2017


CROSSREFS

Cf. A014085.
Sequence in context: A119707 A052938 A302391 * A243852 A025532 A195459
Adjacent sequences: A140111 A140112 A140113 * A140115 A140116 A140117


KEYWORD

nonn


AUTHOR

Philippe Lallouet (philip.lallouet(AT)orange.fr), May 08 2008


EXTENSIONS

Corrected, edited and extended by T. D. Noe, Sep 25 2008


STATUS

approved



