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A090901
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a(n) = floor[geometric mean of first n factorials].
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2
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1, 1, 2, 4, 8, 17, 38, 91, 230, 605, 1661, 4735, 13998, 42795, 135021, 438826, 1466690, 5033778, 17716515, 63865399, 235547709, 887938469, 3418054843, 13424588130, 53753996494, 219278318407, 910679550679, 3848136018924, 16534775039068, 72206065899240
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OFFSET
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1,3
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LINKS
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FORMULA
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MAPLE
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a := n -> mul(k!^(1/n), k=1..n):
prec := n -> max(10, ceil(log(2*Pi*n)/2+n*(log(n/exp(1))))):
seq(floor(evalf(a(n), prec(n))), n=1..100); # Peter Luschny, Nov 27 2015
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MATHEMATICA
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Module[{nn=30, fs}, fs=Range[nn]!; Table[Floor[GeometricMean[Take[fs, n]]], {n, nn}]] (* Harvey P. Dale, Nov 27 2015 *)
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PROG
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(PARI) a(n) = default(realprecision, 2*n); floor(prod(i=2, n, i!)^(1/n));
(Magma) a:=[]; f:=1; P:=1; for n in [1..100] do f*:=n; P*:=f; g:=Floor(P^(1/n)); while true do d:=g^n-P; if d gt 0 then g-:=Ceiling((1.0*d)*g/P/n); else d:=P-(g+1)^n; if d ge 0 then g+:=Ceiling((1.0*d)*g/P/n); else break; end if; end if; end while; a[n]:=g; end for; a; // Jon E. Schoenfield, Nov 27 2015
(Sage)
def a(n): # Throws an error if result could not be computed exactly.
prec = max(53, ceil(0.75*ceil((log(2*pi*n)/2+n*(log(n/exp(1)))))))
rif = RealIntervalField(prec)
r = rif(prod(factorial(k)^(1/n) for k in (1..n)))
return r.unique_floor()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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