Sum-free sequence

In mathematics, a sum-free sequence is an increasing positive integer sequence

$\{n_k\}_{k\in\mathbb N}$

such that for each $k$ , $n k$ is never a sum of preceding elements of the same sequence.

This definition is due to Paul Erdős, who was interested in finding sum-free sequences with a large sum of reciprocals.

An easy example of such a sequence

1, 2, 4, 8, 16, ...