AHSME 1970 Problem 4

Let $S$ be the set of all numbers which are the sum of the squares of three consecutive integers. Then we can say that $\text{(A) No member of S is divisible by } 2 \\ \text{(B) No member of S is divisible by } 3 \text{ but some member is divisible by } 11 \\ \text{(C) No member of S is divisible by } 3 \text{ or } 5 \\ \text{(D) No member of S is divisible by } 3 \text{ or } 7 \\ \text{(E) None of these}$