2

Part of 2012 BMT Spring

Problems(2)

Spring Round (2012) #2

Source:

Find the smallest number with exactly 28 divisors.

number theoryprime factorizationpactorial

2012 BMT Team 2

Source:

\prod_{k=1}^{254}\log_{k+1}(k + 2)^{u_k}

u_k = \begin{cases}- k & \text{if} \,\, k \,\, \text{is odd}\\ \frac{1}{k-1} & \text{if} \,\, k \,\, \text{is even} \end{cases}