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 A049614 n! divided by its squarefree kernel. 25
 1, 1, 1, 1, 4, 4, 24, 24, 192, 1728, 17280, 17280, 207360, 207360, 2903040, 43545600, 696729600, 696729600, 12541132800, 12541132800, 250822656000, 5267275776000, 115880067072000, 115880067072000, 2781121609728000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Also product of composite numbers less than or equal to n. - Benoit Cloitre, Aug 18 2002 Also n! divided by n primorial (or n!/n#). - Cino Hilliard, Mar 26 2006 From Alexander R. Povolotsky and Peter J. C. Moses, Aug 27 2007: (Start) It appears that a(n) = smallest positive number m such that the sequence b(n) = { m (i^1 + 1!) (i^2 + 2!) ... (i^n + n!) / n! : i >= 0 } takes integral values. [It would be nice to have a proof of this! - N. J. A. Sloane] Cf. A064808 (for n=2), A131682 (for n=3), A131683 (for n=4), A131527 (for n=5), A131684 (for n=6), A131528. See also A129995, A131685. (End) It appears that every term > 4 is divisible by 24. - Alexander R. Povolotsky, Oct 18 2007 The above comment is correct since each term divides the next. - Charles R Greathouse IV, Jan 16 2012 When n is not a prime number, then a(n)=m*n, where m is some integer >0; such a(n) make up the A036691 Otherwise, when n is a prime number, then a(n)=a(k), where k is the largest nonprime number preceding n (k mul(k, k=select(isprime, [\$1..n])); A049614 := n -> factorial(n)/primorial(n); seq(A049614(i), i=0..24); # Peter Luschny, Feb 16 2013 MATHEMATICA Table[n! / Product[ Prime[i], {i, 1, PrimePi[n]}], {n, 1, 24}] PROG (PARI) a(n)=prod(i=1, n, i^if(isprime(i), 0, 1)) (PARI) a(n)=n!/prod(i=1, primepi(n), prime(i)) \\ Charles R Greathouse IV, Aug 30 2012 CROSSREFS Cf. A000142, A002110, A003418, A034386, A045948, A048148, A036691, A036691. Sequence in context: A270456 A088304 A131978 * A269186 A058166 A092897 Adjacent sequences:  A049611 A049612 A049613 * A049615 A049616 A049617 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Oct 07 2007 Offset set to 0, a(0)=1 prepended to data, Peter Luschny, Feb 16 2013 STATUS approved

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Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)