HMMT November 2014 U25

What is the smallest positive integer $n$ which cannot be written in any of the following forms?

• $n=1+2+\cdots+k$ for a positive integer $k$.
• $n=p^{k}$ for a prime number $p$ and integer $k$.
• $n=p+1$ for a prime number $p$.
• $n=p q$ for some distinct prime numbers $p$ and $q$