Question 78
Consider a positive integer $N$ with exactly 6 positive divisors $d_1, \ldots, d_6$ such that $1 = d_1 \lt d_2 \lt d_3 \lt d_4 \lt d_5 \lt d_6 = N$. Call such an integer $N$ good if the sum $d_4 + d_5$ is divisible by the sum $d_2 + d_3$.
a) Find the smallest positive integer $N$ which has exactly 6 positive divisors and which is not good.
b) Prove that there are infinitely many positive integers $N$ all with exactly 6 positive divisors and all not good.
a) Find the smallest positive integer $N$ which has exactly 6 positive divisors and which is not good.
b) Prove that there are infinitely many positive integers $N$ all with exactly 6 positive divisors and all not good.