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

Author

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

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A085056.

Programs

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} ] ]

Formula

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

Extensions

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