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
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
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