DNA shared by octopuses and modern humans
Octopuses have more chromosomes and genes

Octopuses have 28 chromosomes, and 33,638 protein-coding genes (Albertin et al 2015).
Humans have 23 chromosomes, and 20,365 protein-coding genes (Uniprot).

Octopuses had an expansion of genes in only a few protein families

There is a large number of C2H2 zinc-finger proteins (C2H2 ZNFs) (~1800), interleukin-17-like genes (IL17-like), G-protein-coupled receptors (GPCRs), chitinases and sialins paralogues in the octopus genome. 

However, there does not exist a comprehensive analysis of orthologous proteins in the octopus that I can find.
This means that although we can say that there are thousands of genes we only observe in octopuses, there is currently no study comparing orthologues that exist in both humans and octopuses.