[seqfan] A property of k-almost primes, but also A006039?

[Peter Munn]

For all k, the set of k-almost primes has the property "all positive
integers are either a divisor or multiple of at least one member, but no
member divides another member".

I've come to think {A006039}, the set of primitive nondeficient numbers,
also has this property, and can see a likely route to prove it; but maybe
I don't need to, as this seems close to the mainstream and could be
well-known. So, does anyone here know?; and does the property have an
established name?

Meanwhile, I have drafted A337814, "the smallest primitive nondeficient
number that divides n or is a multiple of n".

Best regards,

Peter