

A306904


The geometric mean of the first n integers, rounded to the nearest integer.


1



1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 25, 25, 25
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OFFSET

1,3


COMMENTS

a(n) is the least k such that (k1/2)^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*k1)^n < t do od:
last:= k1;
Res:= Res, last;
od:
Res; # Robert Israel, May 05 2019


MATHEMATICA

Array[Round[#!^(1/#)] &, 68] (* Michael De Vlieger, Mar 31 2019 *)


PROG

(PARI) a(n) = round(n!^(1/n)); \\ Michel Marcus, May 05 2019


CROSSREFS

Cf. A000142, A061375 (floor instead of round), A214046.
Sequence in context: A077113 A143796 A245473 * A057362 A214046 A085269
Adjacent sequences: A306901 A306902 A306903 * A306905 A306906 A306907


KEYWORD

nonn


AUTHOR

Robin Powell, Mar 15 2019


EXTENSIONS

Corrected by Robert Israel, May 05 2019


STATUS

approved



