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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Squarefree factorials: a(1) = 1, a(n+1) = a(n)* largest squarefree divisor of (n+1). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 28 2004
LCM over all partitions of n of the product of the part sizes in the partition. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 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
| 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
| Index entries for sequences related to lcm's
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FORMULA
| Partial products of A007947.
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MAPLE
| 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
| a[0] = 1; a[n_] := a[n] = a[n-1] First @ Select[Reverse @ Divisors[n], SquareFreeQ, 1]; Array[a, 22, 0] (* From Jean-François Alcover, May 04 2011 *)
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PROG
| (PARI) a(n)=local(f); f=n>=0; if(n>1, forprime(p=2, n, f*=p^(n\p))); f
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CROSSREFS
| Sequence in context: A182862 A072938 A160274 * A068625 A162935 A051451
Adjacent sequences: A048800 A048801 A048802 * A048804 A048805 A048806
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KEYWORD
| nonn,nice
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Apr 15 1999.
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EXTENSIONS
| Entry improved by comments from Michael Somos, Nov 24, 2001
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