Search: id:A002808
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%I A002808 M3272 N1322
%S A002808 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,
%T A002808 35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,
%U A002808 63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88
%N A002808 The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
%C A002808 The natural numbers 1,2,... are divided into three sets: 1 (the unit), 
               the primes (A000040) and the composite numbers (A002808).
%C A002808 The number of composite numbers <= n (A065855) = n - pi(n) (A000720) 
               - 1.
%C A002808 m is composite iff sigma(m)+phi(m)>2m. - Farideh Firoozbakht (mymontain(AT)yahoo.com), 
               Jan 27 2005
%C A002808 The composite numbers have the semiprimes A001358 as primitive elements.
%C A002808 Numbers that have more than one prime factor. - Juri-Stepan Gerasimov 
               (2stepan(AT)rambler.ru), Sep 01 2009
%C A002808 d(n)>2 [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 17 2009]
%C A002808 Smallest nonprime>nth nonprime. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 29 2009]
%C A002808 Number of prime divisors of n (counted with multiplicity)>1. [From Juri-Stepan 
               Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009]
%D A002808 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 2.
%D A002808 A. E. Bojarincev, Asymptotic expressions for the n-th composite number, 
               Univ. Mat. Zap. 6:21-43 (1967). - In Russian.
%D A002808 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 2.
%D A002808 L. Panaitopol, Some Properties of the Series of Composed Numbers, J. 
               Inequalities in Pure and Applied Mathematics. 2(2): Article 38, 2000.
%D A002808 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               51.
%D A002808 J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions 
               of prime numbers, Illinois J. Math. 6: 64-94 (1962).
%D A002808 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002808 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002808 N. J. A. Sloane, <a href="b002808.txt">Table of n, a(n) for n = 1..17737</
               a> [composites up to 20000]
%H A002808 C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=Composite">
               Composite Numbers</a>
%H A002808 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CompositeNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A002808 <a href="http://jipam.vu.edu.au">J. Inequalities in Pure and Applied 
               Mathematics.</a>
%H A002808 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%p A002808 t := []: for n from 2 to 20000 do if isprime(n) then else t := [op(t),
               n]; fi; od: t;
%p A002808 remove(isprime,[$3..89]); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 19 2007
%p A002808 A002808 := proc(n) local n ; if n = 1 then 4; else for a from procname(n-1)+1 
               do if not isprime(a) then return a; end if; end do ; end if; end 
               proc; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 27 2009]
%t A002808 Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] 
               + 1]; Array[Composite, 71] (from Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Jan 13 2006)
%t A002808 Select[Range[100], ! PrimeQ[ # ] && ! (# == 1) && ! (# == 0) &] - Stefan 
               Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 30 2006 [Corrected 
               by Barbarel Tres Mil, Feb 28 2009]
%o A002808 (PARI) A002808(n)={for(k=0,primepi(n),isprime(n++)&k--);n} [From M. F. 
               Hasler (MHasler(AT)univ-ag.fr), Oct 31 2008]
%o A002808 (PARI) A002808(n)={ my(k=-1); while( -n + n += -k + k=primepi(n),); n} 
               [From M. F. Hasler (mhasler(AT)univ-ag.fr), Nov 11 2009]
%Y A002808 Cf. A000040, A018252, A008578, A065090.
%Y A002808 a(n) = A136527(n, n).
%Y A002808 Cf. A000005, A001222. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 30 2009]
%Y A002808 Sequence in context: A167376 A133576 A088224 this_sequence A018252 A141468 
               A077091
%Y A002808 Adjacent sequences: A002805 A002806 A002807 this_sequence A002809 A002810 
               A002811
%K A002808 nonn,nice,easy,core,new
%O A002808 1,1
%A A002808 N. J. A. Sloane (njas(AT)research.att.com).

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