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Old 2015-07-06, 19:45   #6
davar55
 
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May 2004
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Since the sum of the smaller factors of 2^n equals 1 + 2 + 4 + ... + 2^(n-1) = 2^n - 1
it is never equal to 2^n, hence 2^n is never perfect.

But I like Batalov's parity explanation better.
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