We say that $A\subset \mathbb{N}$ is an essential component if $d_s(A+B)>d_s(B)$ for every $B\subset \mathbb{N}$ with $0<d_s(B)<1$ where $d_s$ is the Schnirelmann density.
Is $B=\{2^m3^n : m,n\geq 0\}$ an essential component?
This page was last edited 23 January 2026.
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