$d(n) = 8$

We can see that every positive integer of the form $p^{7}$ , where $p$ is a prime, has exactly 8 divisors. Since there are an infinite amount of primes, the answer is an infinite amount.

$Every\quad positive\quad integer\quad in\quad the\quad form\quad { a }^{ 1 }{ b }^{ 1 }{ c }^{ 1 },\quad { d }^{ 3 }{ e }^{ 1 }or\quad f^{ 7 }\quad \\ where\quad a,b,c,d,e\quad and\quad f\quad are\quad prime\quad has\quad 8\quad divisors,\\ because\quad there\quad is\quad an\quad infinite\quad amount\quad ofprimes$

The number of factors of a number x = p1^a1 * p2^a2 * p3^a3..... pn^an where pi is a prime number are (a1+1) (a2+1) .....*(an+1) . So any number of the form p^7 will have 8 factors