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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<n). - Alexander R. Povolotsky, Aug 21 2012

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

Index to divisibility sequences

Index entries for sequences related to factorial numbers

FORMULA

a(n) = A000142(n)/A034386(n).

EXAMPLE

n = 11: 11! = 39916800 = 2310*17280 and 2310=2*3*5*7*11.

MAPLE

primorial := n -> 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

Labos Elemer

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.)