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I've just read this interesting article: http://arxiv.org/pdf/1101.4470.pdf

Where I found this graph representing $N(n)$ the number of occurrences of every integer $n$ in the Sloane encyclopedia of integer sequence (OEIS):

I would like the list of values of $N(n)$ for every integer $n$ up to $5050$.

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The OEIS hosts a page

https://oeis.org/stripped.gz

which has all the terms listed in each sequence (but not the b-files). You should be able to download this, split off unused parts, and produce a graph that fits your needs with whatever software you're most comfortable with.

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