A faster Divisors function

*To*: mathgroup at smc.vnet.net*Subject*: [mg22890] A faster Divisors function*From*: Julian Aguirre Estibalez <mtpagesj at lg.ehu.es>*Date*: Tue, 4 Apr 2000 22:40:58 -0400 (EDT)*Organization*: Universidad del Pais Vasco/Euskal Herriko Unibertsitatea*Sender*: owner-wri-mathgroup at wolfram.com

Dear group, I need to find the divisors of a large collection of integers, all of them having small prime factors. An example is In[22]:= n = 5910740121125371424569009155900; Mathematica factorizes it without problems: In[23]:= FactorInteger[n] // Timing Out[23]= {0. Second, {{2, 2}, {3, 2}, {5, 2}, {7, 2}, {11, 1}, {23, 1}, {37, 1}, {79, 1}, {179, 1}, {191, 1}, {223, 1}, {239, 1}, {269, 1}, {419, 1}, {457, 1}, {1931, 1}}} But when trying to compute Divisors[n], I stopped the calculation after one hour. I have written my own divisors function: MyDivisors[n_Integer]:=With[{f=FactorInteger[n]}, Sort at Fold[Flatten@Outer[Times, #1, #2]&, {1}, First/@f^Range[0, Last/@f]]] In[32]:=Length at MyDivisors[n] // Timing Out[32]={16.7333 Second, 331776} As you can see, it is fast, but uses a lot of memory. Of course, it works well with numbers that can be easily factorized, which is always the case with the problem I am working in. Now my question. Can any of you suggest a better way of improving the speed or diminishing the memory rquirements of MyDivisors? Thanks, Julian Aguirre | Voice: +34 946012659 Departamento de Matematicas | Fax: +34 944648500 Universidad del Pais Vasco | Postal: Aptdo. 644, 48080 Bilbao, Spain | email: mtpagesj at lg.ehu.es

**Follow-Ups**:**Re: A faster Divisors function***From:*Hartmut Wolf <hwolf@debis.com>