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

#*****************************************************************************80
#
## SIGMA_VALUES returns some values of the Sigma function.
#
#  Discussion:
#
#    SIGMA(N) is the sum of the distinct divisors of N, including 1 and N.
#
#    In Mathematica, the function can be evaluated by:
#
#      DivisorSigma[1,n]
#
#  First values:
#
#     N  SIGMA(N)
#
#     1    1
#     2    3
#     3    4
#     4    7
#     5    6
#     6   12
#     7    8
#     8   15
#     9   13
#    10   18
#    11   12
#    12   28
#    13   14
#    14   24
#    15   24
#    16   31
#    17   18
#    18   39
#    19   20
#    20   42
#
#  Formula:
#
#    SIGMA(U*V) = SIGMA(U) * SIGMA(V) if U and V are relatively prime.
#
#    SIGMA(P^K) = ( P^(K+1) - 1 ) / ( P - 1 ) if P is prime.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    21 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 Sigma function.
#
#    Output, integer C, the value of the Sigma function.
#
  import numpy as np

  n_max = 20

  c_vec = np.array ( ( \
     1,    3,    4,    7,    6,   12,    8,   15,   13,   18, \
    72,  128,  255,  176,  576, 1170,  618,  984, 2232, 2340 ))

  n_vec = np.array ( ( \
      1,   2,   3,   4,   5,   6,   7,   8,   9,   10, \
     30, 127, 128, 129, 210, 360, 617, 815, 816, 1000 ))

  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 sigma_values_test ( ):

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

  print ( '' )
  print ( 'SIGMA_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  SIGMA_VALUES stores values of the SIGMA function.' )
  print ( '' )
  print ( '             N    SIGMA(N)' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, c = sigma_values ( n_data )

    if ( n_data == 0 ):
      break

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

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