cp's OEIS Frontend

A085056 (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.

%I A085056 #23 Aug 23 2014 13:44:36
%S A085056 1,1,1,2,2,2,2,8,24,24,24,48,48,48,48,384,384,1152,1152,2304,2304,
%T A085056 2304,2304,9216,46080,46080,414720,829440,829440,829440,829440,
%U A085056 13271040,13271040,13271040,13271040,79626240,79626240,79626240,79626240
%N A085056 (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 A085056 Vincenzo Librandi, <a href="/A085056/b085056.txt">Table of n, a(n) for n = 1..200</a>
%F A085056 a(1)=1, a(n)=a(n-1)*n/(n's prime factors).
%F A085056 a(1) = 1, a(n+1) = a(n)*{(n)/(the largest squarefree divisor of n)}. - _Amarnath Murthy_, Nov 28 2004
%F A085056 a(n) = prod_{i=1..n} A003557(i). - _Tom Edgar_, Mar 24 2014
%e A085056 a(9) = (4*6*8*9)/((2)*(2*3)*(2)*(3)) = 24.
%p A085056 A085056 := proc(n) local S,i;
%p A085056 S := A003557(n); for i from 2 to n do
%p A085056 S[i] := S[i] * S[i-1]; od; S end: # _Peter Luschny_, Jun 29 2009
%t A085056 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 A085056 (Sage)
%o A085056 q=50 # change q for more terms
%o A085056 R=[n/prod([x for x in prime_divisors(n)]) for n in [1..q]]
%o A085056 [prod(R[0:i+1]) for i in [0..q-1]] # _Tom Edgar_, Mar 24 2014
%Y A085056 Cf. A084744.
%Y A085056 Cf. A003557. [From _Peter Luschny_, Jun 29 2009]
%K A085056 nonn
%O A085056 1,4
%A A085056 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003
%E A085056 More terms from _Ray Chandler_ and _Robert G. Wilson v_, Jun 27 2003