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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 (list; graph; refs; listen; history; text; internal format)
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: A086615 A081124 A340776 * A101516 A118928 A325921

Adjacent sequences:  A090898 A090899 A090900 * A090902 A090903 A090904

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

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Last modified April 15 09:32 EDT 2021. Contains 342977 sequences. (Running on oeis4.)