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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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%I #23 Aug 23 2014 13:44:36

%S 1,1,1,2,2,2,2,8,24,24,24,48,48,48,48,384,384,1152,1152,2304,2304,

%T 2304,2304,9216,46080,46080,414720,829440,829440,829440,829440,

%U 13271040,13271040,13271040,13271040,79626240,79626240,79626240,79626240

%N (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.

%H Vincenzo Librandi, <a href="/A085056/b085056.txt">Table of n, a(n) for n = 1..200</a>

%F a(1)=1, a(n)=a(n-1)*n/(n's prime factors).

%F a(1) = 1, a(n+1) = a(n)*{(n)/(the largest squarefree divisor of n)}. - _Amarnath Murthy_, Nov 28 2004

%F a(n) = prod_{i=1..n} A003557(i). - _Tom Edgar_, Mar 24 2014

%e a(9) = (4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.

%p A085056 := proc(n) local S,i;

%p S := A003557(n); for i from 2 to n do

%p S[i] := S[i] * S[i-1]; od; S end: # _Peter Luschny_, Jun 29 2009

%t 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} ]

%o (Sage)

%o q=50 # change q for more terms

%o R=[n/prod([x for x in prime_divisors(n)]) for n in [1..q]]

%o [prod(R[0:i+1]) for i in [0..q-1]] # _Tom Edgar_, Mar 24 2014

%Y Cf. A084744.

%Y Cf. A003557. [From _Peter Luschny_, Jun 29 2009]

%K nonn

%O 1,4

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003

%E More terms from _Ray Chandler_ and _Robert G. Wilson v_, Jun 27 2003