The $abc$-conjecture states that if $a,b,c$ are positive, relatively prime integers satisfying $a+b=c$, then the product of the primes dividing $abc$ (the radical of $abc$) is $\gg_\varepsilon c^{1-\varepsilon}$ for every $\varepsilon>0$.

We know several examples of $abc$-triples that refute the stronger assertion that the radical of $abc$ is $\gg c$. One example I have seen involves taking $a=1$, $b=2^n-1$, and $c=2^n$, so that the radical of $abc$ is twice the radical of $2^n-1$. By taking $n$ highly composite - say **the least common multiple of the first $k$ integers** - one forces $2^n-1$ to be divisible by **lots of squares of primes** (those not exceeding $k$, in this case), which implies that the radical of $2^n-1$ is $\ll 2^n/n$. That is, the radical of $abc$ is $\ll c/\log c$.

I'd like to cite this example in a paper I'm writing. Can someone tell me where to find it in the literature? I'd love the original citation, but even an accessible source that explicitly works out the upper bound $\ll c/\log c$ for the radical would suffice.

(Note that I don't need to be pointed to other examples of good $abc$-triples. I've put a couple of phrases above in boldface to emphasize the specific example I'm hoping to cite.)