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Can we generate divisors($n^2$) in case that we already have divisors(n) ? or at least can we predict how many integers are in divisors($n^2$) ?
while divisors(n) is the list of integers (not necessarily primes) which divide n.

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    Look at the table here and compare numbers that relate to your question. What do you notice? Is it 'always' possible?http://en.wikipedia.org/wiki/Table_of_divisors2012-11-23
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    It seems to me that you mean the phrase "divisors(n)" as the result of a computer command in some language similar to Mathematica, which will happily produce an ordered list of divisors, once it succeeds in factoring the number. You really should give some examples to clarify this. I give an answer based on this reading of your question.2012-11-23

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