A075070 a(n) = n-th compositorial number / (product of those primes which divide the n-th compositorial number).

1, 2, 4, 32, 288, 576, 6912, 13824, 207360, 3317760, 59719680, 1194393600, 25082265600, 50164531200, 1203948748800, 30098718720000, 60197437440000, 1625330810880000, 45509262704640000, 1365277881139200000

Offset: 0

Author

Amarnath Murthy, Sep 08 2002

Keywords

• nonn

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).

Examples

			a(0) = 1, a(5) = (4*6*8*9*10)/(2*3*5) = 576, 10 is the fifth composite number.
		

Crossrefs

Cf. A002808.

Programs

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}]

Formula

A036691/(prime factors of A036691)

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