

A061375


Integer part of geometric mean of first n positive integers.


2



1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27
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OFFSET

1,4


COMMENTS

a(n) < (n+1)/2 for n > 1 by the AMGM (arithmeticgeometric mean) inequality.
Also, largest integer m such that m^n <= n!.  M. F. Hasler, Mar 07 2009


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = floor((n!)^(1/n)); (n!)^(1/n) ~ e^(1) (n+log(2 Pi n)/2) + O(log(n)^2/n) as n > infinity.


EXAMPLE

a(7) = floor((7!)^(1/7)) = floor(5040^(1/7)) = floor(3.380015...) = 3.


MATHEMATICA

Table[IntegerPart[GeometricMean[Range[n]]], {n, 80}] (* Harvey P. Dale, Mar 05 2014 *)


PROG

(PARI) A061375(n)=sqrtn(n!, n)\1 \\ M. F. Hasler, Mar 07 2009
(PARI) { default(realprecision, 100); f=1; for (n=1, 1000, f*=n; write("b061375.txt", n, " ", sqrtn(f, n)\1) ) } \\ Harry J. Smith, Jul 22 2009


CROSSREFS

Sequence in context: A057366 A189663 A341440 * A029920 A100719 A057354
Adjacent sequences: A061372 A061373 A061374 * A061376 A061377 A061378


KEYWORD

nonn


AUTHOR

Amarnath Murthy, May 02 2001


EXTENSIONS

Edited by Franklin T. AdamsWatters, May 18 2010


STATUS

approved



