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Search: id:A119861
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| A119861 |
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Number of distinct prime factors of the odd Catalan numbers A038003(n). |
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+0
1
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| 0, 1, 3, 6, 11, 20, 36, 64, 117, 209, 381, 699, 1291, 2387, 4445, 8317, 15645, 29494
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A038003[n] = A000108[2^n-1] = binomial(2^(n+1)-2, 2^n-1)/(2^n). a(1) = 0 because A038003[1] = 1. a(2) = 1 because A038003[2] = 5. a(3) = 3 because A038003[3] = 429 = 3*11*13. a(4) = 6 because A038003[4] = 9694845 = 3^2*5*17*19*23*29.
Odd Catalan numbers are listed in A038003[n] = A000108[2^n-1] = binomial(2^(n+1)-2, 2^n-1)/(2^n).
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LINKS
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Eric Weisstein's World of Mathematics, Catalan Number.
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FORMULA
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a(n) = Length[ FactorInteger[ Binomial[ 2^(n+1)-2, 2^n-1] / (2^n) ]].
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MAPLE
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with(numtheory): c:=proc(n) options operator, arrow: binomial(2*n, n)/(n+1) end proc: seq(nops(factorset(c(2^n-1))), n=1..15); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 24 2007
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MATHEMATICA
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Table[Length[FactorInteger[Binomial[2^(n+1)-2, 2^n-1]/(2^n)]], {n, 1, 15}]
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CROSSREFS
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Cf. A038003, A000108, A120274, A120275.
Cf. A000108 = Catalan Number. Cf. A038003 = Odd Catalan numbers. Cf. A120274, A120275, A119908, A094389.
Sequence in context: A077855 A054887 A019302 this_sequence A018075 A125896 A094989
Adjacent sequences: A119858 A119859 A119860 this_sequence A119862 A119863 A119864
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 31 2006, Oct 11 2007
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EXTENSIONS
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a(16)-a(18) found by Robert G. Wilson, May 15 2007.
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