Let τ (n) denote the number of positive divisors of n and σ(n) denote the sum...

Let τ (n) denote the number of positive divisors of n and σ(n) denote the sum of the positive divisors of n (as in the notes).

(a) Evaluate τ (1500) and σ(8!).

(b) Verify that τ (n) = τ (n + 1) = τ (n + 2) = τ (n + 3) holds for n = 3655 and 4503.

(c) When n = 14, n = 206 and n = 957, show that σ(n) = σ(n + 1).

Expert Solution

Colby Messinger answered 2 years ago

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