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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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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| 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 (amarnath_murthy(AT)yahoo.com), Nov 28 2004
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EXAMPLE
| a(9) = (4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.
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MAPLE
| Contribution from Peter Luschny (peter(AT)luschny.de), Jun 29 2009: (Start)
A085056 := proc(n) local S, i;
S := A003557(n); for i from 2 to n do
S[i] := S[i] * S[i-1]; od; S end: (End)
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MATHEMATICA
| 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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CROSSREFS
| Cf. A084744.
Cf. A003557. [From Peter Luschny (peter(AT)luschny.de), Jun 29 2009]
Sequence in context: A100943 A152660 A058787 * A156538 A165466 A175392
Adjacent sequences: A085053 A085054 A085055 * A085057 A085058 A085059
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), Jun 26 2003
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2003
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