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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) < (n+1)/2 for n > 1 by the AM-GM (arithmetic-geometric 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. Adams-Watters, May 18 2010

STATUS

approved

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Last modified August 5 10:38 EDT 2021. Contains 346466 sequences. (Running on oeis4.)