Re: The prime factors of n.

• To: mathgroup at smc.vnet.net
• Subject: [mg32729] Re: The prime factors of n.
• From: lalu_bhatt at yahoo.com (Bhuvanesh)
• Date: Thu, 7 Feb 2002 05:10:31 -0500 (EST)
• References: <a3qqjj\$27t\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Robert G. Wilson v" <rgwv at kspaint.com> wrote:

> Hello all,
>
>         I wish to receive a list of prime factors of n not in the form
> returned by FactorInteger. Instead I want only the primes the number of
> times they appear. As an example I will use 72. FactorInteger[72] gives
> { {2,3}, {3,2} }. I wish the list would read { 2, 2, 2, 3, 3 }. Is the
> following the best that I can do? f[n_Integer] := Module[{a =
> FactorInteger[n], b = {}}, While[Length[a] > 0, Do[b = Append[b, a[[1,
> 1]]], {a[[1, 2]]}]; a = Drop[a, 1]]; b] .
>
> See
> http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=037276
>
> Sincerely yours,
>
> Robert G. "Bob" Wilson, V

Well, here's a simple alternate way that is clearer for me:

In[1]:= f[n_Integer] := Flatten[Map[Table[#[[1]], {#[[2]]}]&, FactorInteger[n]]]

In[2]:= f[72]

Out[2]= {2, 2, 2, 3, 3}

--
Bhuvanesh,
Wolfram Research.

```

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