Is sum of divisors function a one-to-one function?

Suppose $N$ is a positive integer that can be expressed as a product of distinct prime numbers: $N = p_1 \times p_2 \times \cdots \times p_n.$ Then the sum of all the positive divisors of $N$ is $(p_1 + 1) \times (p_2 +1 ) \times \cdots \times (p_n + 1) .$ Now, suppose that $M$ is a positive integer the sum of whose positive divisors is $(3 + 1) \times (5+1) \times (7 +1) .$ Does that mean $M$ must be equal to $3\times5\times7?$