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Search: id:A084744
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| A084744 |
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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. |
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+0
2
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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More precisely the denominator equals the product of the largest square-free divisors of composite numbers up to n.
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FORMULA
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a(1)=1, a(n)=a(n-1)*n/(n's prime factors).
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EXAMPLE
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a(4) = (1*4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.
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MAPLE
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A084744 := proc(n) sort(convert(convert(A085056(n), set), list)) end: [From Peter Luschny (peter(AT)luschny.de), Jun 29 2009]
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MATHEMATICA
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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} ]
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CROSSREFS
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Cf. A084056.
Adjacent sequences: A084741 A084742 A084743 this_sequence A084745 A084746 A084747
Sequence in context: A138387 A007346 A062247 this_sequence A122547 A152132 A009059
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 26 2003
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2003
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