Erdős-Granville-Pomerance-Spiro Conjecture

The Erdős-Granville-Pomerance-Spiro conjecture asserts that if a set of positive integers has natural density zero, then

also has natural density zero (Erdős et al. 1990). Here is the divisor function giving the sum of the positive divisors of , so is its restricted divisor function.

The conjecture remains open (Pollack et al. 2018, Bloom 2026). The restriction keeps the restricted divisor function positive. The conclusion concerns natural density, rather than logarithmic density.

This is problem 955 in the Erdős problems collection (Bloom 2026).