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

1, 1, 1, 2, 2, 2, 2, 2, 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, 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, 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

Offset

1,4

Links

Table of n, a(n) for n=1..105.

Example

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.

Maple

A069624 := proc(n)
    local s, k, a ;
    s := {} ;
    for k from 2 do
        a := floor(n^(1/k)) ;
        s := s union {a} ;
        if a = 1 then
            break;
        end if;
    end do:
    nops(s) ;
end proc: # R. J. Mathar, May 19 2014

Mathematica

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}]

Crossrefs

Cf. A071913.

Sequence in context: A343437 A348242 A105517 * A230774 A056813 A125269

Adjacent sequences: A069621 A069622 A069623 * A069625 A069626 A069627

Keyword

nonn

Author

Amarnath Murthy, Mar 27 2002

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Jun 14 2002

Definition corrected by Robert Israel, May 18 2014

a(8) corrected by Sean A. Irvine, May 08 2024

Status

approved