|
| |
|
|
A049614
|
|
n! divided by its squarefree kernel.
|
|
20
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| Also product of composite numbers less than or equal to n. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 18 2002
Also, except for the first term, n! divided by n primorial (or n!/n#). - Cino Hilliard (hillcino368(AT)gmail.com), Mar 26 2006
Comment from Alexander R. Povolotsky (pevnev(AT)juno.com) and Peter J. C. Moses (mows(AT)mopar.freeserve.co.uk), Aug 27 2007: 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 (njas(AT)research.att.com)] 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.
It appears that every term > 4 is divisible by 3 - Alexander R. Povolotsky (pevnev(AT)juno.com), Oct 18 2007
The above comment is correct since each term divides the next. [Charles R Greathouse IV, Jan 16 2012]
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n = 1..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
|
|
|
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))
|
|
|
CROSSREFS
| Cf. A000142, A002110, A003418, A034386, A045948, A048148, A036691.
Sequence in context: A075219 A088304 A131978 * A058166 A092897 A171633
Adjacent sequences: A049611 A049612 A049613 * A049615 A049616 A049617
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 07 2007
|
| |
|
|
