OFFSET
1,3
COMMENTS
a(n) is the least k such that (k-1/2)^n < n!. - Robert Israel, May 05 2019
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = round(n!^(1/n)).
a(n) ~ n/e + log(n)/(2*e). - Robert Israel, May 05 2019
EXAMPLE
a(5) is the 5th root of the product of the first 5 integers (approx. 2.605171) rounded up to 3.
MAPLE
Res:= 1: last:= 1: v:= 1:
for n from 2 to 100 do
v:= n*v; t:= 2^n*v;
for k from last while (2*k-1)^n < t do od:
last:= k-1;
Res:= Res, last;
od:
Res; # Robert Israel, May 05 2019
MATHEMATICA
Array[Round[#!^(1/#)] &, 68] (* Michael De Vlieger, Mar 31 2019 *)
Table[Round[GeometricMean[Range[n]]], {n, 70}] (* Harvey P. Dale, Mar 19 2023 *)
PROG
(PARI) a(n) = round(n!^(1/n)); \\ Michel Marcus, May 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Powell, Mar 15 2019
EXTENSIONS
Corrected by Robert Israel, May 05 2019
STATUS
approved