%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