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Is the integer n odd?

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Source: — Data Sufficiency |
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by JJJooe » Wed Aug 26, 2009 8:19 pm
n=p1^(m1)p2^(m2)...pk^(mk)，
here p means prime factor
m means mathematical power
then
the number of all the factors of n equals
(m1+1)*(m2+2)...*(mk+1)

so this question becomes simple
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by JJJooe » Wed Aug 26, 2009 9:15 pm
only when n is an odd integer,which has no 2 as its prime factor，the prime factors of 2n include 2 plus the prime factors of n. according to the above formula for calculating the total positive integers of a positive integer，the number of positive integers by which 2n is divisible equals twice that by which n is divisible.
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by JJJooe » Wed Aug 26, 2009 9:16 pm
the correct answer is B
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