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A090901
a(n) = floor[geometric mean of first n factorials].
2
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
OFFSET
1,3
LINKS
Peter Luschny and Jon E. Schoenfield, Table of n, a(n) for n = 1..871 (First 100 terms from Peter Luschny)
FORMULA
a(n) = floor(A000178(n)^(1/n)).
MAPLE
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
MATHEMATICA
Module[{nn=30, fs}, fs=Range[nn]!; Table[Floor[GeometricMean[Take[fs, n]]], {n, nn}]] (* Harvey P. Dale, Nov 27 2015 *)
PROG
(PARI) a(n) = default(realprecision, 2*n); floor(prod(i=2, n, i!)^(1/n));
vector(500, n, a(n)) \\ Altug Alkan, Nov 27 2015
(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()
[a(n) for n in (1..100)] # Peter Luschny, Nov 28 2015
CROSSREFS
Cf. A090902.
Sequence in context: A357903 A081124 A340776 * A101516 A118928 A325921
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Dec 12 2003
EXTENSIONS
Corrected and extended by N. J. A. Sloane, Oct 26 2004
More terms from Emeric Deutsch, Apr 13 2005
Corrected by Harvey P. Dale, Nov 27 2015
STATUS
approved