HarmonicNumber

Let a be an odd integer, show that
$(1 + 2 + \dots + n) / (1^a + 2^a + \dots + n^a)$
While I was working on this problem I discovered again how powerful Mathematica actually is.
It is simply possible to calculate the sum $(1^a + 2^a + \dots + n^a)$ by $H(n,-a)$. Or in InputForm: HarmonicNumber(n,-a).