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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
OFFSET
1,2
COMMENTS
More precisely the denominator equals the product of the largest squarefree divisors of composite numbers up to n.
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
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