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I'm trying to make a list of rules where every integer is replaced with a string of it's prime factorization:

$$ \left( \begin{array}{c} 1\to \left\{1^1\right\} \\ 2\to \left\{2^1\right\} \\ 3\to \left\{3^1\right\} \\ 4\to \left\{2^2\right\} \\ 5\to \left\{5^1\right\} \\ 6\to \left\{2^1,3^1\right\} \\ 7\to \left\{7^1\right\} \\ 8\to \left\{2^3\right\} \\ 9\to \left\{3^2\right\} \\ 10\to \left\{2^1,5^1\right\} \\ 11\to \left\{11^1\right\} \\ \end{array} \right) $$

However, I don't want the rules to be lists. I want 6 to map to $2^1\cdot 3^1$... and so on. How do I accomplish this?

The factorization code is:

FactorInt[x_]:=Module[{},
(Superscript @@@ FactorInteger[x])
]
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  • 1
    $\begingroup$ Analogously to: mathematica.stackexchange.com/q/133083/5478? $\endgroup$ – Kuba May 2 '18 at 16:47
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    $\begingroup$ What's Collatz? Is that really needed here? $\endgroup$ – Henrik Schumacher May 2 '18 at 16:59
  • $\begingroup$ It isn't. I'm just going to ask another question later since this one is answered. $\endgroup$ – Robbie May 2 '18 at 17:01
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Something like this?

factorInteger[x_Integer] := Row[Superscript @@@ FactorInteger[x]]
factorInteger /@ Range@10 // Column

enter image description here

To get the results in a list of rules you can use:

With[{numbers = Range@10},
  Thread[Rule[numbers, factorInteger /@ numbers]]
  ] // Column

enter image description here

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