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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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21
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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
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LINKS
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FORMULA
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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:
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MATHEMATICA
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PROG
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(Sage)
if n < 2 : return 1
else :
D = divisors(n); D.pop()
(GAP) List([1..30], n->Factorial(n)/Lcm([1..n])); # Muniru A Asiru, Apr 02 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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