Q.

If N denotes the set of all positive integers and if f:NNis defined by fn=the sum of positive divisors of n, then f2k. 3, where k is a positive integer, is 

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a

2k+1-1

b

32k+1-1

c

42k+1-1

d

22k+1-1

answer is D.

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Detailed Solution

f(n) = sum of positive divisors of n

f(2k.3)=sum of divisors of2k 31

            =(1+2+22+ ... + 2k)  (1+3)            =4(2k+1-1)

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