Sums of prime factors
Julia, 95 93 bytes



g(x)=reduce(vcat,map(p-&gt;map(sum,p),partitions([keys(factor(x))...])))
f(a,b)=g(a)∩g(b)!=[]


The primary function is f and it calls a helper function g.

Ungolfed:

function g(x::Integer)
    # Find the sum of each combination of prime factors of the input
    return reduce(vcat, map(p -&gt; map(sum, p), partitions([keys(factor(x))...])))
end

function f(a::Integer, b::Integer)
    # Determine whether there's a nonzero intersection of the factor
    # sums of a and b
    return !isempty(g(a) ∩ g(b))
end


Saved 2 bytes thanks to Darth Alephalpha