cp's OEIS Frontend

The first few sums S(n) = Sum_{k = 1..n} 1/(A000959(k)*A375527(k)) are: 1/2, 5/6, 41/42, 629/630, 57329/57330,

219172589/219172590, 2287458514758689/2287458514758690,

523246645674205487113407810299/523246645674205487113407810300, ..., and the first 10 or 11 of these sums have the form (c-1)/c, where c is an integer. The present sequence gives the denominators.

For the harmonic series analog, A374663, Rémy Sigrist has shown that all the partial sums have that form (see A374983), and for the prime number analog, A375581, it seems that all partial sums except for n = 4 and 6 have this property (see A375521/A375522).