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.

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

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 26 2003

Keywords

• nonn

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A084744.

Cf. A003557. [From Peter Luschny, Jun 29 2009]

Programs

Maple

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: # Peter Luschny, Jun 29 2009

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} ]

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

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, Nov 28 2004

a(n) = prod_{i=1..n} A003557(i). - Tom Edgar, Mar 24 2014

Extensions

More terms from Ray Chandler and Robert G. Wilson v, Jun 27 2003