A084744 Product of all composite numbers from 1 to the n-th nonprime number divided by product of all the prime divisors of each of those composite numbers which exceed the previously stated value.

1, 2, 8, 24, 48, 384, 1152, 2304, 9216, 46080, 414720, 829440, 13271040, 79626240, 318504960, 637009920, 1911029760, 15288238080, 107017666560, 535088332800, 1070176665600, 9631589990400, 38526359961600, 77052719923200

Offset

1,2

Comments

More precisely the denominator equals the product of the largest squarefree divisors of composite numbers up to n.

Links

Table of n, a(n) for n=1..24.

Formula

a(1)=1, a(n) = a(n-1)*n/(n's prime factors).

Example

a(4) = (1*4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.

Maple

A084744 := proc(n) sort(convert(convert(A085056(n), set), list)) end: # Peter Luschny, Jun 29 2009

Mathematica

PrimeFactors[ n_Integer ] := Flatten[ Table[ # [ [ 1 ] ], {1} ] & /@ FactorInteger[ n ] ]; a[ 1 ] := 1; a[ n_ ] := a[ n ] = a[ n - 1 ]*n / Times @@ PrimeFactors[ n ]; Union[ Table[ a[ n ], {n, 1, 63} ]

Crossrefs

Cf. A084056.

Sequence in context: A284951 A357635 A171261 * A122547 A152132 A330520

Adjacent sequences: A084741 A084742 A084743 * A084745 A084746 A084747

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003

Extensions

Edited and extended by Robert G. Wilson v, Jun 27 2003

Status

approved