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A069624 Number of different values taken by the integer part of n^(1/k) for all k > 1. 2

%I

%S 1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,

%T 4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,

%U 4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5

%N Number of different values taken by the integer part of n^(1/k) for all k > 1.

%e a(28) = 4, floor[28^(1/2)] = 5, floor[28^1/3] = 3, floor[28^1/4] = 2, floor [28^1/5] = 1= floor[28^1/k, (k > 5)], etc. The distinct values are 1,2,3 and 5.

%p A069624 := proc(n)

%p local s,k,a ;

%p s := {} ;

%p for k from 2 do

%p a := floor(n^(1/k)) ;

%p s := s union {a} ;

%p if a = 1 then

%p break;

%p end if;

%p end do:

%p nops(s) ;

%p end proc: # _R. J. Mathar_, May 19 2014

%t f[n_] := Block[{k = 1}, While[ Floor[n^(1/k)] != 1, k++ ]; k]; Table[ Length[ Union[ Table[ Floor[n^(1/k)], {k, 2, f[n]+1}]]], {n, 1, 105}]

%Y Cf. A071913.

%K nonn

%O 1,4

%A _Amarnath Murthy_, Mar 27 2002

%E Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Jun 14 2002

%E Definition corrected by _Robert Israel_, May 18 2014

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Last modified October 16 16:18 EDT 2019. Contains 328101 sequences. (Running on oeis4.)