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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. 2
1, 2, 8, 24, 48, 384, 1152, 2304, 9216, 46080, 414720, 829440, 13271040, 79626240, 318504960, 637009920, 1911029760, 15288238080, 107017666560, 535088332800, 1070176665600, 9631589990400, 38526359961600, 77052719923200 (list; graph; refs; listen; history; text; internal format)
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: A062247 A284951 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

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Last modified January 20 16:04 EST 2022. Contains 350472 sequences. (Running on oeis4.)