#! /usr/bin/env python
#
def 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:
#
#    20 February 2015
#
#  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.
#
  import numpy as np

  n_max = 20

  c_vec = np.array ( ( \
      1,  -1,  -1,   0,  -1,   1,  -1,   0,   0,   1, \
     -1,   0,  -1,   1,   1,   0,  -1,   0,  -1,   0 ))

  n_vec = np.array ( ( \
      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

  if ( n_max <= n_data ):
    n_data = 0
    n = 0
    c = 0
  else:
    n = n_vec[n_data]
    c = c_vec[n_data]
    n_data = n_data + 1

  return n_data, n, c

def moebius_values_test ( ):

#*****************************************************************************80
#
## MOEBIUS_VALUES_TEST demonstrates the use of MOEBIUS_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'MOEBIUS_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  MOEBIUS_VALUES stores values of the MOEBIUS function.' )
  print ( '' )
  print ( '             N    MOEBIUS(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, c = moebius_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12d  %12d' % ( n, c ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'MOEBIUS_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  moebius_values_test ( )
  timestamp ( )