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Search: id:A002808
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| A002808 |
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The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
(Formerly M3272 N1322)
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+0
415
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| 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The natural numbers 1,2,... are divided into three sets: 1 (the unit), the primes (A000040) and the composite numbers (A002808).
The number of composite numbers <= n (A065855) = n - pi(n) (A000720) - 1.
m is composite iff sigma(m)+phi(m)>2m. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Jan 27 2005
The composite numbers have the semiprimes A001358 as primitive elements.
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 2.
A. E. Bojarincev, Asymptotic expressions for the n-th composite number, Univ. Mat. Zap. 6:21-43 (1967). - In Russian.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2.
L. Panaitopol, Some Properties of the Series of Composed Numbers, J. Inequalities in Pure and Applied Mathematics. 2(2): Article 38, 2000.
J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6: 64-94 (1962).
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 51.
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..17737 [composites up to 20000]
C. K. Caldwell, Composite Numbers
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
J. Inequalities in Pure and Applied Mathematics.
Index entries for "core" sequences
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MAPLE
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t := []: for n from 2 to 20000 do if isprime(n) then else t := [op(t), n]; fi; od: t;
remove(isprime, [$3..89]); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
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MATHEMATICA
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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)
Select[Range[100], ! PrimeQ[ # ] && ! (# == 1) && ! (# == 0) &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 30 2006 [Corrected by Barbarel Tres Mil, Feb 28 2009]
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PROGRAM
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(PARI) A002808(n)={for(k=0, primepi(n), isprime(n++)&k--); n} [From M. F. Hasler (MHasler(AT)univ-ag.fr), Oct 31 2008]
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CROSSREFS
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Cf. A000040, A018252, A008578, A065090.
a(n) = A136527(n, n).
Adjacent sequences: A002805 A002806 A002807 this_sequence A002809 A002810 A002811
Sequence in context: A137353 A133576 A088224 this_sequence A018252 A141468 A077091
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KEYWORD
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nonn,nice,easy,core
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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