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A085056
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(Product of all composite numbers from 1 to n)/ ( product of the prime divisors of all composite numbers up to n). More precisely, denominator = product of the largest squarefree divisors of composite numbers up to n.
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5
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1, 1, 1, 2, 2, 2, 2, 8, 24, 24, 24, 48, 48, 48, 48, 384, 384, 1152, 1152, 2304, 2304, 2304, 2304, 9216, 46080, 46080, 414720, 829440, 829440, 829440, 829440, 13271040, 13271040, 13271040, 13271040, 79626240, 79626240, 79626240, 79626240
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OFFSET
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1,4
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LINKS
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FORMULA
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a(1)=1, a(n)=a(n-1)*n/(n's prime factors).
a(1) = 1, a(n+1) = a(n)*{(n)/(the largest squarefree divisor of n)}. - Amarnath Murthy, Nov 28 2004
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EXAMPLE
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a(9) = (4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.
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MAPLE
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S := A003557(n); for i from 2 to n do
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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 ]; Table[ a[ n ], {n, 1, 40} ]
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PROG
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(Sage)
q=50 # change q for more terms
R=[n/prod([x for x in prime_divisors(n)]) for n in [1..q]]
[prod(R[0:i+1]) for i in [0..q-1]] # Tom Edgar, Mar 24 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003
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EXTENSIONS
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STATUS
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approved
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