TITLE: Has this number-theoretic constant been studied?
QUESTION [11 upvotes]: Unless I made a mistake, the expected value of the largest exponent in the prime factorization of random positive integer (defined in the appropriate way) is $$\eta := \sum_{n=1}^\infty \Big(1-\zeta(n)^{-1}\Big)$$ with the convention $\zeta(1)^{-1} = 0$ (for aesthetics). I was just wondering whether this constant $\eta$ has a name, whether it's been studied, etc..

REPLY [32 votes]: If you calculate it to a few decimals, you find
$$
1.705211140105\ldots
$$
which is enough to locate it in the OEIS.
It's Niven's constant: MathWorld, Wikipedia, OEIS.
As mentioned by GH from MO in the comments, it was in fact proven by Niven in 1969 that the average largest exponent tends to $\eta$.
Since the question is essentially about finding literature related to a given numerical constant, I should probably mention this answer by myself on the other site, exhibiting some other methods (Steven Finch's book Mathematical Constants & how to google the decimals effectively).