Computation Workshop Solution Checker

Divisor Sums

For any positive integer \(n\), let \(D(n)\) be the sum of all positive integer divisors of \(n\) (including \(1\) and \(n\) itself). Let \(P(n)\) be the sum of \(D(i)\) for all \(i = 1,2,3, \ldots ,n\). So for example \(P(3) = D(1)+D(2)+D(3) = 1+3+4 = 8\).

Recursively Defined Sequence

A sequence \((t(0), t(1), t(2), t(3), \ldots) = (2,1,5,13, \ldots)\) begins with \(t(0)=2\) and \(t(1)=1\). Then

• \(t(2) = t(1) + 2t(0)\),
• \(t(3) = t(2) + 2t(1) + 3t(0)\),
• \(t(4) = t(3) + 2t(2) + 3t(1) + 4t(0)\),
• \(\ldots\) and so on.