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A025527
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a(n) = n!/LCM{1,2,...,n} = (n-1)!/LCM{C(n-1,0),C(n-1,1),...,C(n-1,n-1)}.
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15
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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
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OFFSET
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1,4
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COMMENTS
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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=A006093. - Lekraj Beedassy, Aug 03 2006
a(n) are the partial products of A048671(n). [From Peter Luschny, Sep 09 2009]
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LINKS
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Table of n, a(n) for n=1..26.
Index entries for sequences related to lcm's
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FORMULA
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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
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EXAMPLE
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a(5) = 2 as 5!/LCM(1..5) = 120/60 = 2.
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MAPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A003418.
Sequence in context: A196061 A131121 A055772 * A205957 A092144 A224497
Adjacent sequences: A025524 A025525 A025526 * A025528 A025529 A025530
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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