This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049614 #46 Jul 21 2023 19:06:03
%S A049614 1,1,1,1,4,4,24,24,192,1728,17280,17280,207360,207360,2903040,
%T A049614 43545600,696729600,696729600,12541132800,12541132800,250822656000,
%U A049614 5267275776000,115880067072000,115880067072000,2781121609728000,69528040243200000,1807729046323200000
%N A049614 n! divided by its squarefree kernel.
%C A049614 Also product of composite numbers less than or equal to n. - _Benoit Cloitre_, Aug 18 2002
%C A049614 Also n! divided by n primorial (or n!/n#). - _Cino Hilliard_, Mar 26 2006
%C A049614 From _Alexander R. Povolotsky_ and _Peter J. C. Moses_, Aug 27 2007: (Start)
%C A049614 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)
%C A049614 It appears that every term > 4 is divisible by 24. - _Alexander R. Povolotsky_, Oct 18 2007
%C A049614 The above comment is correct since each term divides the next. - _Charles R Greathouse IV_, Jan 16 2012
%C A049614 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
%H A049614 T. D. Noe, <a href="/A049614/b049614.txt">Table of n, a(n) for n = 0..100</a>
%H A049614 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A049614 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A049614 a(n) = A000142(n)/A034386(n).
%e A049614 n = 11: 11! = 39916800 = 2310*17280 and 2310=2*3*5*7*11.
%p A049614 primorial := n -> mul(k, k=select(isprime, [$1..n]));
%p A049614 A049614 := n -> factorial(n)/primorial(n);
%p A049614 seq(A049614(i),i=0..24); # _Peter Luschny_, Feb 16 2013
%t A049614 Table[n!/Product[ Prime[i], {i, PrimePi[n]}], {n, 24}]
%o A049614 (PARI) a(n)=prod(i=1,n,i^if(isprime(i),0,1))
%o A049614 (PARI) a(n)=n!/prod(i=1,primepi(n),prime(i)) \\ _Charles R Greathouse IV_, Aug 30 2012
%o A049614 (Magma)
%o A049614 A049614:= func< n | n le 1 select 1 else Factorial(n)/(&*[NthPrime(j): j in [1..#PrimesUpTo(n)]]) >;
%o A049614 [A049614(n): n in [0..40]]; // _G. C. Greubel_, Jul 21 2023
%o A049614 (SageMath)
%o A049614 def A049614(n): return factorial(n)/product(nth_prime(j) for j in range(1,1+prime_pi(n)))
%o A049614 [A049614(n) for n in range(41)] # _G. C. Greubel_, Jul 21 2023
%Y A049614 Cf. A000142, A002110, A003418, A034386, A036691, A045948, A048148.
%K A049614 nonn
%O A049614 0,5
%A A049614 _Labos Elemer_
%E A049614 Edited by _N. J. A. Sloane_, Oct 07 2007
%E A049614 Offset set to 0, a(0)=1 prepended to data, _Peter Luschny_, Feb 16 2013