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

1,4

Links

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

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

Example

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

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} ]

Prog

(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

Crossrefs

Cf. A084744.

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

Sequence in context: A058787 A353392 A360310 * A371619 A265447 A156538

Adjacent sequences: A085053 A085054 A085055 * A085057 A085058 A085059

Keyword

nonn

Author

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

Extensions

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

Status

approved