70 lines
2.2 KiB
Prolog
70 lines
2.2 KiB
Prolog
% See https://en.wikipedia.org/wiki/Divisor_function
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divisor_sum(N, Total):-
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divisor_sum_prime(N, 2, 2, Total1, 1, N1),
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divisor_sum(N1, 3, Total, Total1).
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divisor_sum(1, _, Total, Total):-
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!.
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divisor_sum(N, Prime, Total, Running_total):-
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Prime * Prime =< N,
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!,
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divisor_sum_prime(N, Prime, Prime, P, 1, M),
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Next_prime is Prime + 2,
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Running_total1 is P * Running_total,
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divisor_sum(M, Next_prime, Total, Running_total1).
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divisor_sum(N, _, Total, Running_total):-
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Total is (N + 1) * Running_total.
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divisor_sum_prime(N, Prime, Power, Total, Running_total, M):-
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0 is N mod Prime,
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!,
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Running_total1 is Running_total + Power,
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Power1 is Power * Prime,
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N1 is N // Prime,
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divisor_sum_prime(N1, Prime, Power1, Total, Running_total1, M).
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divisor_sum_prime(N, _, _, Total, Total, N).
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% See https://en.wikipedia.org/wiki/Aliquot_sequence
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aliquot_sequence(N, Limit, Sequence, Class):-
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aliquot_sequence(N, Limit, [N], Sequence, Class).
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aliquot_sequence(_, 0, _, [], 'non-terminating'):-!.
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aliquot_sequence(_, _, [0|_], [0], terminating):-!.
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aliquot_sequence(N, _, [N, N|_], [], perfect):-!.
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aliquot_sequence(N, _, [N, _, N|_], [N], amicable):-!.
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aliquot_sequence(N, _, [N|S], [N], sociable):-
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memberchk(N, S),
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!.
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aliquot_sequence(_, _, [Term, Term|_], [], aspiring):-!.
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aliquot_sequence(_, _, [Term|S], [Term], cyclic):-
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memberchk(Term, S),
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!.
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aliquot_sequence(N, Limit, [Term|S], [Term|Rest], Class):-
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divisor_sum(Term, Sum),
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Term1 is Sum - Term,
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L1 is Limit - 1,
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aliquot_sequence(N, L1, [Term1, Term|S], Rest, Class).
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write_aliquot_sequence(N, Sequence, Class):-
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writef('%w: %w, sequence:', [N, Class]),
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write_aliquot_sequence(Sequence).
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write_aliquot_sequence([]):-
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nl,
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!.
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write_aliquot_sequence([Term|Rest]):-
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writef(' %w', [Term]),
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write_aliquot_sequence(Rest).
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main:-
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between(1, 10, N),
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aliquot_sequence(N, 16, Sequence, Class),
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write_aliquot_sequence(N, Sequence, Class),
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fail.
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main:-
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member(N, [11, 12, 28, 496, 220, 1184, 12496, 1264460, 790, 909, 562, 1064, 1488]),
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aliquot_sequence(N, 16, Sequence, Class),
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write_aliquot_sequence(N, Sequence, Class),
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fail.
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main.
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