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A075070
a(n) = n-th compositorial number / (product of those primes which divide the n-th compositorial number).
1
1, 2, 4, 32, 288, 576, 6912, 13824, 207360, 3317760, 59719680, 1194393600, 25082265600, 50164531200, 1203948748800, 30098718720000, 60197437440000, 1625330810880000, 45509262704640000, 1365277881139200000
OFFSET
0,2
COMMENTS
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).
FORMULA
A036691/(prime factors of A036691)
EXAMPLE
a(0) = 1, a(5) = (4*6*8*9*10)/(2*3*5) = 576, 10 is the fifth composite number.
MATHEMATICA
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}]
CROSSREFS
Cf. A002808.
Sequence in context: A366365 A247014 A085055 * A144937 A009110 A225170
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 08 2002
EXTENSIONS
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
STATUS
approved