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

#*****************************************************************************80
#
## PHI_VALUES returns some values of the PHI function.
#
#  Discussion:
#
#    PHI(N) is the number of integers between 1 and N which are
#    relatively prime to N.  I and J are relatively prime if they
#    have no common factors.  The function PHI(N) is known as
#    "Euler's totient function".
#
#    By convention, 1 and N are relatively prime.
#
#    In Mathematica, the function can be evaluated by:
#
#      EulerPhi[n]
#
#  First values:
#
#     N  PHI(N)
#
#     1    1
#     2    1
#     3    2
#     4    2
#     5    4
#     6    2
#     7    6
#     8    4
#     9    6
#    10    4
#    11   10
#    12    4
#    13   12
#    14    6
#    15    8
#    16    8
#    17   16
#    18    6
#    19   18
#    20    8
#
#  Formula:
#
#    PHI(U*V) = PHI(U) * PHI(V) if U and V are relatively prime.
#
#    PHI(P^K) = P^(K-1) * ( P - 1 ) if P is prime.
#
#    PHI(N) = N * Product ( P divides N ) ( 1 - 1 / P )
#
#    N = Sum ( D divides N ) PHI(D).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 September 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 PHI function.
#
#    Output, integer C, the value of the PHI function.
#
  import numpy as np

  n_max = 20

  c_vec = np.array ( ( \
      1,   1,   2,   2,   4,   2,   6,   4,   6,   4, \
      8,   8,  16,  20,  16,  40, 148, 200, 200, 648 ))

  n_vec = np.array ( ( \
      1,   2,   3,   4,   5,   6,   7,   8,   9,  10, \
     20,  30,  40,  50,  60, 100, 149, 500, 750, 999 ))

  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 phi_values_test ( ):

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

  print ( '' )
  print ( 'PHI_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PHI_VALUES stores values of the PHI function.' )
  print ( '' )
  print ( '             N    PHI(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, c = phi_values ( n_data )

    if ( n_data == 0 ):
      break

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

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