To my knowledge, this puzzle is not previously published (except by me on google+ recently), but I would be interested to hear of any info otherwise.
This following graph was generated using a simple ruby program and gnuplot. It graphs a "basic/fundamental" number theoretic property of the natural numbers. Can you figure out what it is? Increasingly detailed hints below if you want more help. The answer and further background will be posted as a comment after some time.
"fundamental" as in "fundamental theorem of arithmetic"
one word: prime