The probability distribution of LCM of uniformly distributed integers in {1,…,n}\{1,\ldots,n\}

In the recent paper by Fernandez and Fernandez here on ArXiv, the following formula which was first proved by Diaconis and Erdos appears, on page 2.

For 0<t1 the distribution of the lcm of independent pairs of integers X1,X2 uniformly drawn from {1,,n} satisfies:
P(lcm(X1,X2)tn2)=11ζ(2)1tj=11jt(1ln(jt))j2+Ot(lnnn).

The authors extend these results to k>2, but I am mostly interested in the k=2 case.

My Question: What is the implied tdependent constant in the Ot(lnn/n) term?

Answer

Attribution
Source : Link , Question Author : kodlu , Answer Author : Community

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