Let ? (n) denote the number of positive divisors of n and ?(n)denote the sum of the positive divisors of n (as in the notes).
(a) Evaluate ? (1500) and ?(8!).
(b) Verify that ? (n) = ? (n + 1) = ? (n + 2) = ? (n + 3) holdsfor n = 3655 and 4503.
(c) When n = 14, n = 206 and n = 957, show that ?(n) = ?(n +1).
