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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 (list; graph; refs; listen; history; text; internal format)
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), 611-627.

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: A007456 A119707 A052938 * 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

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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.