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

1, 1, 1, 2, 2, 12, 12, 48, 144, 1440, 1440, 17280, 17280, 241920, 3628800, 29030400, 29030400, 522547200, 522547200, 10450944000, 219469824000, 4828336128000, 4828336128000, 115880067072000, 579400335360000, 15064408719360000

Offset: 1

Author

Clark Kimberling, Dec 11 1999

Keywords

• nonn

Comments

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

a(k) = a(k+1) for k in A006093. - Lekraj Beedassy, Aug 03 2006

Partial products of A048671. - Peter Luschny, Sep 09 2009

Examples

			a(5) = 2 as 5!/lcm(1..5) = 120/60 = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..500
• Liam Solus, Simplices for Numeral Systems, arXiv:1706.00480 [math.CO], 2017. Mentions this sequence.
• Index entries for sequences related to lcm's

Crossrefs

Cf. A000142, A002541, A006093, A003418, A048671, A025529, A205957.

See also A002944, A025537.

Programs

GAP

List([1..30],n->Factorial(n)/Lcm([1..n])); # Muniru A Asiru, Apr 02 2018

Maple

seq(n!/lcm($1..n), n=1..30);
A025527 := proc(n) option remember; `if`(n < 3, 1, ilcm(op(numtheory[divisors](n) minus{1,n}))*A025527(n-1)) end:
seq(A025527(i),i=1..26); # Peter Luschny, Mar 23 2011

Mathematica

Table[n!/Apply[LCM,Range[n]],{n,1,26}] (* Geoffrey Critzer, Jun 17 2013 *)

PARI

a(n)=n!/lcm([2..n]) \\ Charles R Greathouse IV, Mar 06 2014

Sage

def A025527(n) :
    if n < 2 : return 1
    else :
        D = divisors(n); D.pop()
    return lcm(D)*A025527(n-1)
[A025527(i) for i in (1..26)] # Peter Luschny, Feb 03 2012

Formula

a(n) = A000142(n)/A003418(n) = A000254(n)/A025529(n). - Franz Vrabec, Sep 13 2005

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

a(n) = A205957(n), 1 <= n <= 11. - Daniel Forgues, Apr 22 2014

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