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%I #3 Mar 31 2012 13:21:57
%S 2,2,2,2,3,3,3,2,3,4,4,4,4,4,4,4,4,4,4,4,5,5,2,2,3,3,3,5,5,5,5,5,5,5,
%T 2,5,5,5,5,41,42,43,44,45,46,47,2,2,2,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U 6,6,6,6,6,6,6,6,6,4,4,4,4,4,4,4,4,4,4,4,87,88,89,90,91,92,93,94,95,96,97
%N n^(1/a(n)) is the closest to an integer on 2..n with a(n) minimal.
%C The sequence is conjectured to tend to n, as n^(1/n)->1. Is the density of nonnegative entries 0?
%e 5^(1/2)= 2.236067977499789696409173668
%e 5^(1/3)= 1.709975946676696989353108872
%e 5^(1/4)= 1.495348781221220541911898994
%e 5^(1/5)= 1.379729661461214832390063464
%e 5^(1/2) is closest to an integer, so a(5)=2.
%o (PARI) { for (i=2,100, xj=1;xm=0.5; for (j=2,i, x=i^(1/j)*1.0; xf=x-floor(x); if (xf<xm, xm=xf;xj=j); if (1-xf<xm, xm=1-xf;xj=j)); print1(","xj)) }
%K nonn
%O 2,1
%A _Jon Perry_, Mar 19 2004
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