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A075070
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a(n) = n-th compositorial number / (product of those primes which divide the n-th compositorial number).
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1
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1, 2, 4, 32, 288, 576, 6912, 13824, 207360, 3317760, 59719680, 1194393600, 25082265600, 50164531200, 1203948748800, 30098718720000, 60197437440000, 1625330810880000, 45509262704640000, 1365277881139200000
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OFFSET
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0,2
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COMMENTS
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Smallest integer of the form 'Product of first n composite number/ product of first k primes'.
Divide Compositorial(n) by Primorial(k) choosing k to give the smallest integer. (k+1)-th prime does not divide a(n).
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LINKS
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Table of n, a(n) for n=0..19.
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FORMULA
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A036691/(prime factors of A036691)
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EXAMPLE
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a(0) = 1, a(5) = (4*6*8*9*10)/(2*3*5) = 576, 10 is the fifth composite number.
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MATHEMATICA
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Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; PrimeFactors[n_] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; Table[ Product[ Composite[i], {i, 1, n}]/ Times @@ PrimeFactors[ Product[ Composite[i], {i, 1, n}]], {n, 0, 20}]
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CROSSREFS
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Cf. A002808.
Sequence in context: A019060 A247014 A085055 * A144937 A009110 A225170
Adjacent sequences: A075067 A075068 A075069 * A075071 A075072 A075073
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy, Sep 08 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v, Jul 15 2003
Further edited by N. J. A. Sloane, Sep 13 2008 at the suggestion of R. J. Mathar
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STATUS
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approved
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