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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)}. 18
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

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

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

EXAMPLE

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

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 *)

PROG

(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

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

CROSSREFS

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

Sequence in context: A131121 A232853 A055772 * A205957 A092144 A224497

Adjacent sequences:  A025524 A025525 A025526 * A025528 A025529 A025530

KEYWORD

nonn

AUTHOR

Clark Kimberling, Dec 11 1999

STATUS

approved

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Last modified August 22 10:37 EDT 2017. Contains 290946 sequences.