Claims

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1982_01_01_erdos: Erdős, recalling the problem in a 1982 survey, states that the divergence of G(n) for almost all n is trivial; the site records Tao's two-line proof through the bound G(n) at least tau(n/m)/m for a divisor m > 1.

1983_01_01_erdos_tenenbaum: Erdős and Tenenbaum prove that the sum of G(n) for n up to x is (1 + o(1)) x log x and that G(n) is at least tau(n)/(2P(n)) for the least prime factor P(n) of n, which gives G(n) tending to infinity for almost all n.

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