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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
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
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: A189663 A341440 A355028 * A029920 A100719 A057354
KEYWORD
nonn
AUTHOR
Amarnath Murthy, May 02 2001
EXTENSIONS
Edited by Franklin T. Adams-Watters, May 18 2010
STATUS
approved