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A048803
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a(0) = 1, a(1) = 1; for n > 1, a(n) = lcm( 1, 2, ..., n, a(1)*a(n-1), a(2)*a(n-2), ..., a(n-1)*a(1) ).
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6
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1, 1, 2, 6, 12, 60, 360, 2520, 5040, 15120, 151200, 1663200, 9979200, 129729600, 1816214400, 27243216000, 54486432000, 926269344000, 5557616064000, 105594705216000, 1055947052160000, 22174888095360000, 487847538097920000
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OFFSET
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0,3
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COMMENTS
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Squarefree factorials: a(1) = 1, a(n+1) = a(n)* largest squarefree divisor of (n+1). - Amarnath Murthy, Nov 28 2004
LCM over all partitions of n of the product of the part sizes in the partition. - Franklin T. Adams-Watters, May 04 2010
a(n) is the product of the lcm of the set of prime factors of k over the range k = 1..n. - Peter Luschny, Jun 10 2011
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REFERENCES
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Paul-Jean Cahen and Jean-Luc Chabert, Integer-valued Polynomials, AMS, Providence, RI, 1997. Math. Rev. 98a:13002. See p. 246.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..500
Index entries for sequences related to lcm's
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FORMULA
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Partial products of A007947.
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MAPLE
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A048803 := proc(n) local i; mul(ilcm(op(numtheory[factorset](i))), i=1..n) end; seq(A048803(i), i=0..22); # Peter Luschny, Jun 10 2011
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = a[n-1] First @ Select[Reverse @ Divisors[n], SquareFreeQ, 1]; Array[a, 22, 0] (* Jean-François Alcover, May 04 2011 *)
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PROG
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(PARI) a(n)=local(f); f=n>=0; if(n>1, forprime(p=2, n, f*=p^(n\p))); f
(Haskell)
a048803 n = a048803_list !! n
a048803_list = scanl (*) 1 a007947_list
-- Reinhard Zumkeller, Jul 01 2013
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CROSSREFS
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Sequence in context: A182862 A072938 A160274 * A068625 A162935 A051451
Adjacent sequences: A048800 A048801 A048802 * A048804 A048805 A048806
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KEYWORD
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nonn,nice
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AUTHOR
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Christian G. Bower, Apr 15 1999
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EXTENSIONS
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Entry improved by comments from Michael Somos, Nov 24 2001
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STATUS
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approved
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