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A025527 a(n) = n!/lcm{1,2,...,n} = (n-1)!/lcm{C(n-1,0), C(n-1,1), ..., C(n-1,n-1)}.

%I A025527 #81 Sep 04 2019 10:42:27
%S A025527 1,1,1,2,2,12,12,48,144,1440,1440,17280,17280,241920,3628800,29030400,
%T A025527 29030400,522547200,522547200,10450944000,219469824000,4828336128000,
%U A025527 4828336128000,115880067072000,579400335360000,15064408719360000
%N A025527 a(n) = n!/lcm{1,2,...,n} = (n-1)!/lcm{C(n-1,0), C(n-1,1), ..., C(n-1,n-1)}.
%C A025527 a(n) = a(n-1) iff n is prime. Thus a(1)=a(2)=a(3)=1 is the only triple in this sequence. - _Franz Vrabec_, Sep 10 2005
%C A025527 a(k) = a(k+1) for k in A006093. - _Lekraj Beedassy_, Aug 03 2006
%C A025527 Partial products of A048671. - _Peter Luschny_, Sep 09 2009
%H A025527 Alois P. Heinz, <a href="/A025527/b025527.txt">Table of n, a(n) for n = 1..500</a>
%H A025527 Liam Solus, <a href="https://arxiv.org/abs/1706.00480">Simplices for Numeral Systems</a>, arXiv:1706.00480 [math.CO], 2017. Mentions this sequence.
%H A025527 <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F A025527 a(n) = A000142(n)/A003418(n) = A000254(n)/A025529(n). - _Franz Vrabec_, Sep 13 2005
%F A025527 log a(n) = n log n - 2n + O(n/log^4 n). (The error term can be improved. On the Riemann Hypothesis it is O(n^k) for any k > 1/2.) - _Charles R Greathouse IV_, Oct 16 2012
%F A025527 a(n) = A205957(n), 1 <= n <= 11. - _Daniel Forgues_, Apr 22 2014
%F A025527 Conjecture: a(A006093(n)) = phi(A000142(A006093(n))) / phi(A003418(A006093(n))), where phi is the Euler totient function. - _Fred Daniel Kline_, Jun 03 2017
%e A025527 a(5) = 2 as 5!/lcm(1..5) = 120/60 = 2.
%p A025527 seq(n!/lcm($1..n), n=1..30);
%p A025527 A025527 := proc(n) option remember; `if`(n < 3, 1, ilcm(op(numtheory[divisors](n) minus{1,n}))*A025527(n-1)) end:
%p A025527 seq(A025527(i),i=1..26); # _Peter Luschny_, Mar 23 2011
%t A025527 Table[n!/Apply[LCM,Range[n]],{n,1,26}] (* _Geoffrey Critzer_, Jun 17 2013 *)
%o A025527 (Sage)
%o A025527 def A025527(n) :
%o A025527     if n < 2 : return 1
%o A025527     else :
%o A025527         D = divisors(n); D.pop()
%o A025527     return lcm(D)*A025527(n-1)
%o A025527 [A025527(i) for i in (1..26)] # _Peter Luschny_, Feb 03 2012
%o A025527 (PARI) a(n)=n!/lcm([2..n]) \\ _Charles R Greathouse IV_, Mar 06 2014
%o A025527 (GAP) List([1..30],n->Factorial(n)/Lcm([1..n])); # _Muniru A Asiru_, Apr 02 2018
%Y A025527 Cf. A000142, A002541, A006093, A003418, A048671, A025529, A205957.
%Y A025527 See also A002944, A025537.
%K A025527 nonn
%O A025527 1,4
%A A025527 _Clark Kimberling_, Dec 11 1999