Q:

Trying to find how to find how many prime factors have an odd exponent?

Hi I am doing a question for Mathematica and I'm having difficulties.The question is in the prime factorization of n, how many prime factors have an odd exponent? The given n is shown below (very large)
n = 142065190756865870282488068105667182577501738882057884851974445654\
3423237742166396721779311436580070305999267257391443148780739279119880\
6036362837818906515298335482078702168477375932413656083756056968587479\
3126870900658037035232621234336490924847626041243376077191947718333766\
2139781422597901111260689303906160406976537383552880685721245542814240\
4381640394269606051500
The first step I did was to show the prime factorization of the given n,
pf=FactorInteger[n] 
but I'm having trouble knowing how to extract the odd exponents and list them in the output.  

A:

but I'm having trouble knowing how to extract the odd exponents and
  list them in the output.

For purpose of showing this, there is no need to use such a large number (it is taking too long).
n = 2434500;
pf = FactorInteger[n]

gives
{{2, 2}, {3, 2}, {5, 3}, {541, 1}}

So all what you have to do is use Cases to select the odd exponents
 Cases[pf,{x_,y_}/;OddQ[y]:>HoldForm[x^y]]

Or if you just want the exponent
 Cases[pf,{x_,y_}/;OddQ[y]:>y]

And if you want to remove duplicate odd exponents that show up, you could always call Union on the result.

