function [ n_data, n, c ] = moebius_values ( n_data )

%*****************************************************************************80
%
%% MOEBIUS_VALUES returns some values of the Moebius function.
%
%  Discussion:
%
%    MU(N) is defined as follows:
%
%      MU(N) = 1 if N = 1;
%              0 if N is divisible by the square of a prime;
%              (-1)^K, if N is the product of K distinct primes.
%
%    In Mathematica, the function can be evaluated by:
%
%      MoebiusMu[n]
%
%  First values:
%
%     N  MU(N)
%
%     1    1
%     2   -1
%     3   -1
%     4    0
%     5   -1
%     6    1
%     7   -1
%     8    0
%     9    0
%    10    1
%    11   -1
%    12    0
%    13   -1
%    14    1
%    15    1
%    16    0
%    17   -1
%    18    0
%    19   -1
%    20    0
%
%    As special cases, MU(N) is -1 if N is a prime, and MU(N) is 0
%    if N is a square, cube, etc.
%
%  Formula:
%
%    The Moebius function is related to Euler's totient function:
%
%      PHI(N) = Sum ( D divides N ) MU(D) * ( N / D ).
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    19 September 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Milton Abramowitz and Irene Stegun,
%    Handbook of Mathematical Functions,
%    US Department of Commerce, 1964.
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
%    first call.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    Output, integer N, the argument of the Moebius function.
%
%    Output, integer C, the value of the Moebius function.
%
  n_max = 20;

  c_vec = [ ...
      1,  -1,  -1,   0,  -1,   1,  -1,   0,   0,   1, ...
     -1,   0,  -1,   1,   1,   0,  -1,   0,  -1,   0 ];

  n_vec = [ ...
      1,   2,   3,   4,   5,   6,   7,   8,   9,  10, ...
     11,  12,  13,  14,  15,  16,  17,  18,  19,  20 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    c = 0;
  else
    n = n_vec(n_data);
    c = c_vec(n_data);
  end

  return
end
