2... 1/2 THEN 3... 1/6 THEN 5 ....1/15 and so on. And So On?

The excellent graphic novelPrime Suspects: The Anatomy of Integers and Permutationsby Andrew Granville and Jennifer Granville, illustrated by Robert J Lewis,(I wrote a review of this graphic novel, for SIGACT News, here.)has an appendix, which is not in graphic-novel form, where they describe some of the math talked about in the graphic novel. Here is a quote that intrigued me for two reasons2 is the smallest prime factor of half of the integers,3 is the smallest prime factor of one-sixth of the integers,5 is the smallest prime factor of one-fifteenth of the integers,and so fourth.Intrigue One: and so fourth ? Really? That would indicate that it is easy to know what the next fraction is. Is it easy? That depends on your definition of easy.Intrigue Two: What is the next fraction? What is the fraction asymptotically? I worked both of these out fairly fast; however, I don't think and so fourth is appropriate.We derive the 1/15 for 5. 1/5 of all numbers have a factor of 5. Of those, only…