/* 

  Sum of divisors in Picat.


  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

main => go.

go =>
  foreach(N in 1..60)
    printf("%d,%d\n",N,sum_divisors(N))
  end,  
  
  nl.


go2 =>
  foreach(N in 1..60)
    printf("%d,%d\n",N,sum_divisors2(N))
  end,  
  
  nl.


% Including 1 and N
sum_divisors2(1) = 1.
sum_divisors2(N) = sum_divisors(N)+N.


% This recursive version is slightly faster than sum_divisors2/1.
% Not including N
table
sum_divisors(N) = Sum =>
  sum_divisors(2,N,1,Sum).

sum_divisors(I,N,Sum0,Sum), I > floor(sqrt(N)) =>
  Sum = Sum0.

% I is a divisor of N
sum_divisors(I,N,Sum0,Sum), N mod I == 0 =>
  Sum1 = Sum0 + I,
  (I != N div I -> 
    Sum2 = Sum1 + N div I 
    ; 
    Sum2 = Sum1
  ),
  sum_divisors(I+1,N,Sum2,Sum).

% I is no divisor of N.
sum_divisors(I,N,Sum0,Sum) =>
  sum_divisors(I+1,N,Sum0,Sum).