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Problem of the Day #149: Seungln’s favorite function August 15, 2011

Posted by Albert in : potd , trackback

Seungln’s favorite function, $f(n)$, is defined to be the number of subsets (including $\varnothing$) of $\{1,2,3,\ldots,n\}$ for which the product of the elements of the subset is less than or equal to $n$. Seungln can easily bash $f(25) = 86$ (after all, there’s only $33,554,432$ subsets to check), but he’s having trouble with $f(30)$ and higher. Help him find $$\sum\limits_{n=30}^{40}f(n)$$

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