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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.
5
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
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
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