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

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

are the only valid solutions.
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