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 A048803 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) ). 11
 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; text; internal format)
 OFFSET 0,3 COMMENTS 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 REFERENCES Paul-Jean Cahen and Jean-Luc Chabert, Integer-valued Polynomials, AMS, Providence, RI, 1997. Math. Rev. 98a:13002. See p. 246. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..500 Bakir Farhi, On the derivatives of the integer-valued polynomials, arXiv:1810.07560 [math.NT], 2018. FORMULA Partial products of A007947. a(n) = Prod_{p prime} p^floor(n/p). See Farhi link p. 16. - Michel Marcus, Oct 18 2018 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A182862 A072938 A160274 * A068625 A162935 A051451 Adjacent sequences:  A048800 A048801 A048802 * A048804 A048805 A048806 KEYWORD nonn,nice AUTHOR Christian G. Bower, Apr 15 1999 EXTENSIONS Entry improved by comments from Michael Somos, Nov 24 2001 STATUS approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)