Re: Peculiar behaviour of Mathematica code

*To*: mathgroup at smc.vnet.net*Subject*: [mg57964] Re: Peculiar behaviour of Mathematica code*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Tue, 14 Jun 2005 05:10:29 -0400 (EDT)*Organization*: University of Washington*References*: <d8jlau$srs$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Tony King" <mathstutoring at ntlworld.com> wrote in message news:d8jlau$srs$1 at smc.vnet.net... >I have some Mathematica code which I borrowed from the Divisors package. > This code should return True if its argument is semiperfect and False if > it > is not. > > Here is the code > > SemiperfectQ[n_Integer?Positive]:=Module[{d=Most[Divisors[n]]}, > > n==Plus@@#&/@(Or@@Rest[Subsets[d]]) > > ] > > This seems to work fine if the argument is composite. However, if the > input > is prime it returns {False} rather than False. > Here is a different approach which is generally faster: SemiperfectQ[n_Integer?Positive] := Block[{x}, Coefficient[Expand[Times @@ (1 + x^Most[Divisors[n]])], x^n] > 0] Both approaches essentially compute the power set of the divisors, and so the time grows exponentially with the number of divisors. If you are interested in numbers with a lot of divisors, you may wish to investigate algorithms which don't compute the power set (e.g. backtracking). > Similarly the code for returning True if a number is weird behaves in the > same way > > WeirdQ[n_Integer?Positive]:=DivisorSigma[1,n]>2n&& > > n!=Plus@@#&/@(And@@Rest[Subsets[Most[Divisors[n]]]]) > > Any ideas how these codes could be modified to return False (rather than > {False}) for prime inputs > Once you have SemiperfectQ working, then it's simple: WeirdQ[n_Integer?Positive]:=DivisorSigma[1,n]>2n && !SemiperfectQ[n] > Thank you > > Tony > Carl Woll Wolfram Research