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 A066265 a(n) = number of semiprimes < 10^n. 27
 0, 3, 34, 299, 2625, 23378, 210035, 1904324, 17427258, 160788536, 1493776443, 13959990342, 131126017178, 1237088048653, 11715902308080, 111329817298881, 1061057292827269, 10139482913717352, 97123037685177087, 932300026230174178, 8966605849641219022, 86389956293761485464 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from the first nonzero term the sequence is identical to A036352. - Hugo Pfoertner, Jul 22 2003 LINKS Eric Weisstein's World of Mathematics, Semiprime FORMULA (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). - Robert G. Wilson v, May 16 2005 EXAMPLE Below 10 there are three semiprimes: 4 (2*2), 6 (2*3) and 9 (3*3). MATHEMATICA 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}] (* Robert G. Wilson v, May 16 2005 *) SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@ i] - i + 1, {i, PrimePi@ Sqrt@ n}]; Array[ SemiPrimePi[10^# - 1] &, 14, 0] (* Robert G. Wilson v, Jan 21 2015 *) PROG (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 (Perl) use Math::Prime::Util qw/:all/; use integer; sub countsp { my(\$k, \$sum, \$pc)=(\$_[0]-1, 0, 1); prime_precalc(60_000_000); forprimes { \$sum += prime_count(\$k/\$_) + 1 - \$pc++; } int(sqrt(\$k)); \$sum; } foreach my \$n (0..16) { say "\$n: ", countsp(10**\$n); } # Dana Jacobsen, May 11 2014 CROSSREFS Cf. A001358, A064911, A072000, A036352 (identical starting from a(2)), A220262, A292785. Sequence in context: A121077 A024396 A246384 * A268802 A284891 A231593 Adjacent sequences:  A066262 A066263 A066264 * A066266 A066267 A066268 KEYWORD nonn AUTHOR Patrick De Geest, Dec 10 2001 EXTENSIONS 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 a(17)-a(18) from Dana Jacobsen, May 11 2014 a(19)-a(21) from Henri Lifchitz, Jul 04 2015 STATUS approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)