#! /usr/bin/env python
#
def mertens_values ( n_data ):

#*****************************************************************************80
#
## MERTENS_VALUES returns some values of the Mertens function.
#
#  Discussion:
#
#    The Mertens function M(N) is the sum from 1 to N of the Moebius
#    function MU.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    M Deleglise, J Rivat,
#    Computing the Summation of the Moebius Function,
#    Experimental Mathematics,
#    Volume 5, 1996, pages 291-295.
#
#    Eric Weisstein,
#    CRC Concise Encyclopedia of Mathematics,
#    CRC Press, 2002,
#    Second edition,
#    ISBN: 1584883472,
#    LC: QA5.W45.
#
#  Parameters:
#
#    Input, integer N_DATA, indicates the index of the previous test data
#    returned, or is 0 if this is the first call.  For repeated calls,
#    set the input value of N_DATA to the output value of N_DATA
#    from the previous call.
#
#    Output, integer N_DATA, the index of the test data.
#
#    Output, integer N, the argument of the Mertens function.
#
#    Output, integer C, the value of the Mertens function.
#
  import numpy as np

  n_max = 15

  c_vec = np.array ( ( \
      1,   0,  -1,   -1,  -2,  -1,  -2,  -2,   -2,  -1, \
     -2,  -2,   1,    2, -23 ))

  n_vec = np.array ( ( \
      1,   2,   3,   4,   5,   6,   7,   8,   9,  10, \
     11,  12,  100, 1000, 10000 ))

  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 mertens_values_test ( ):

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

  print ( '' )
  print ( 'MERTENS_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  MERTENS_VALUES stores values of the MERTENS function.' )
  print ( '' )
  print ( '             N    MERTENS(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, c = mertens_values ( n_data )

    if ( n_data == 0 ):
      break

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

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