Data commit

Task/Aliquot-sequence-classifications/Picat/aliquot-sequence-classifications.picat

@@ -0,0 +1,56 @@
+divisor_sum(N) = R =>
+    Total = 1,
+    Power = 2,
+    % Deal with powers of 2 first
+    while (N mod 2 == 0)
+        Total := Total + Power,
+        Power := Power*2,
+        N := N div 2
+    end,
+    % Odd prime factors up to the square root
+    P = 3,
+    while (P*P =< N)
+        Sum = 1,
+        Power1 = P,
+        while (N mod P == 0)
+            Sum := Sum + Power1,
+            Power1 := Power1*P,
+            N := N div P
+        end,
+        Total := Total * Sum,
+        P := P+2
+    end,
+    % If n > 1 then it's prime
+    if N > 1 then
+        Total := Total*(N + 1)
+    end,
+    R = Total.
+
+% See https://en.wikipedia.org/wiki/Aliquot_sequence
+aliquot_sequence(N,Limit,Seq,Class) =>
+    aliquot_sequence(N,Limit,[N],Seq,Class).
+
+aliquot_sequence(_,0,_,Seq,Class) => Seq = [], Class = 'non-terminating'.
+aliquot_sequence(_,_,[0|_],Seq,Class) => Seq = [0], Class = terminating.
+aliquot_sequence(N,_,[N,N|_],Seq,Class) => Seq = [], Class = perfect.
+aliquot_sequence(N,_,[N,_,N|_],Seq,Class) => Seq = [N], Class = amicable.
+aliquot_sequence(N,_,[N|S],Seq,Class), membchk(N,S) =>
+    Seq = [N], Class = sociable.
+aliquot_sequence(_,_,[Term,Term|_],Seq,Class) => Seq = [], Class = aspiring.
+aliquot_sequence(_,_,[Term|S],Seq,Class), membchk(Term,S) =>
+    Seq = [Term], Class = cyclic.
+aliquot_sequence(N,Limit,[Term|S],Seq,Class) =>
+    Seq = [Term|Rest],
+    Sum = divisor_sum(Term),
+    Term1 is Sum - Term,
+    aliquot_sequence(N,Limit-1,[Term1,Term|S],Rest,Class).
+
+main =>
+    foreach (N in [11,12,28,496,220,1184,12496,1264460,790,909,562,1064,1488,15355717786080,153557177860800])
+        aliquot_sequence(N,16,Seq,Class),
+        printf("%w: %w, sequence: %w ", N, Class, Seq[1]),
+        foreach (I in 2..len(Seq), break(Seq[I] == Seq[I-1]))
+            printf("%w ", Seq[I])
+        end,
+        nl
+    end.