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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A100943 A152660 A058787 * A265447 A156538 A249768

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

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Last modified September 20 18:26 EDT 2018. Contains 315240 sequences. (Running on oeis4.)