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(D) The given number is $N = a^1 b^2 c^2 d^1 e^1$.Since $a, b, c, d, e$ are prime integers,the total number of divisors of $N$ is given by the product

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$71$

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(D) The given number is $N = a^1 b^2 c^2 d^1 e^1$.Since $a, b, c, d, e$ are prime integers,the total number of divisors of $N$ is given by the product of (exponent + $1$) for each prime factor.Total number of divisors $= (1 + 1)(2 + 1)(2 + 1)(1 + 1)(1 + 1) = 2 	imes 3 	imes 3 	imes 2 	imes 2 = 72$.We need to find the number of divisors excluding $1$ as a factor.Number of divisors excluding $1 = 72 - 1 = 71$.

If $a, b, c, d, e$ are prime integers,then the number of divisors of $a b^2 c^2 d e$ excluding $1$ as a factor is:

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