Puzzling Partitions

Let $$D(n)$$ be the number of ways of adding distinct positive integers to sum to $$n$$.

Let $$O(n)$$ be the number of ways of adding odd positive integers to sum to $$n$$.

Let $$D = D(2016)$$ and $$O = O(2016)$$.

Which is bigger?

Examples

For example $$D(5) = 3$$ since

\begin{align} 5 &= 5 \\ &= 2+ 3 \\ &= 1 + 4 \end{align}

and $$O(4) = 2$$ since

\begin{align} 4 &= 1 + 1 + 1 + 1 \\ &= 1 + 3 \end{align}

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