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A049614 n! divided by its squarefree kernel. 32
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, 69528040243200000, 1807729046323200000 (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
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, PrimePi[n]}], {n, 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
(Magma)
A049614:= func< n | n le 1 select 1 else Factorial(n)/(&*[NthPrime(j): j in [1..#PrimesUpTo(n)]]) >;
[A049614(n): n in [0..40]]; // G. C. Greubel, Jul 21 2023
(SageMath)
def A049614(n): return factorial(n)/product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
[A049614(n) for n in range(41)] # G. C. Greubel, Jul 21 2023
CROSSREFS
Sequence in context: A270456 A088304 A131978 * A269186 A058166 A092897
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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)