The number of positive divisors of the form $2n + 1(n\ge 1)$  of the integer 120 is

240 is divisible by $4n + 2$ or 120 is divisible by $2n + 1.$

Number of the form $(2n + 1), n\in I$ are all odd natural numbers.

Thus we have to find all odd numbers dividing 120. 
These numbers are 1, 3, 5, 15.
Hence, number of divisors = 4.
if $n\ge 1$ number of divisors are 3