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

0,2

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).

Links

Table of n, a(n) for n=0..19.

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

Adjacent sequences: A075067 A075068 A075069 * A075071 A075072 A075073

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