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A066265
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Number of semiprimes < 10^n.
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24
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0, 3, 34, 299, 2625, 23378, 210035, 1904324, 17427258, 160788536, 1493776443, 13959990342, 131126017178, 1237088048653, 11715902308080, 111329817298881, 1061057292827269
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OFFSET
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0,2
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COMMENTS
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Apart from the first nonzero term the sequence is identical to A036352. - Hugo Pfoertner, Jul 22 2003
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LINKS
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Table of n, a(n) for n=0..16.
Eric Weisstein's World of Mathematics, Semiprime
Index entries for sequences related to numbers of primes in various ranges
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FORMULA
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(1/2)*( Pi(10^(n/2)) + Sum_{i=1..Pi(10^n)} Pi( (10^n-1)/P_i) ) = Sum_{i=1..Pi(sqrt(10^n))} Pi( (10^n-1)/P_i ) - Binomial( Pi(sqrt(10^n)), 2) (from Robert G. Wilson v, May 16 2005)
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EXAMPLE
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Below 10 there are three semiprimes: 4 (2*2), 6 (2*3) and 9 (3*3).
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MATHEMATICA
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f[n_] := Sum[ PrimePi[(10^n - 1)/Prime[i]], {i, PrimePi[ Sqrt[10^n]]}] - Binomial[ PrimePi[ Sqrt[10^n]], 2]; Do[ Print[ f[n]], {n, 0, 14}] (from Robert G. Wilson v, May 16 2005)
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PROG
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(PARI) a(n)=my(s); forprime(p=2, sqrt(10^n), s+=primepi((10^n-1)\p)); s-binomial(primepi(sqrt(10^n)), 2) \\ Charles R Greathouse IV, Apr 23 2012
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CROSSREFS
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Cf. A001358, A064911, A072000, A036352 (identical starting from a(2)).
Sequence in context: A141789 A121077 A024396 * A134491 A045727 A105713
Adjacent sequences: A066262 A066263 A066264 * A066266 A066267 A066268
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KEYWORD
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nonn
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AUTHOR
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Patrick De Geest, Dec 10 2001.
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EXTENSIONS
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More terms from Hugo Pfoertner, Jul 22 2003
a(14) from Robert G. Wilson v, May 16 2005
a(15)-a(16) from Donovan Johnson, Mar 18 2010
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STATUS
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approved
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