powers(Factors,N,Powers) :-
	sort(Factors,SFactors),
	pair(SFactors,Pairs),
	first_powers(N,Pairs,Powers).

pair([],[]).
pair([X|R],[(X,X)|S]) :- pair(R,S).

first_powers(N,[(Power,Factor)|PFs],[Power|Powers]) :-
	( N == 1 ->
	    Powers = []
	;
	    N1 is N - 1,
	    remove_power(Power,PFs,PFs1),
	    Power1 is Power * Factor,
	    sorted_insert(PFs1,(Power1,Factor),PFs2),
	    first_powers(N1,PFs2,Powers)
	).

remove_power(Power,PFsIn,PFsOut) :-
	( PFsIn = [(Power,_)|RestPFsIn] ->
	    remove_power(Power,RestPFsIn,PFsOut)
	;
	    PFsOut = PFsIn
	).

sorted_insert([],X,[X]).
sorted_insert([A|R],X,Out) :-
	( A @< X ->
	    Out = [A|RestOut],
	    sorted_insert(R,X,RestOut)
	;
	    Out = [X,A|R]
	).