asking help in terminology

[Emeric Deutsch]

Dear seqfans,

A question of terminology:

I have a sequence, say A (it does not contain 1). It
has the property that all multiples of all terms of
A are in A. What is the best way to describe this?
Closed under multiplication by positive integers?

Let me call a term of A primitive if no proper divisor
of A is in A. The sequence S of the primitive terms of A
is infinite. What is a good term for this subsequence?
Kernel of A? The prime kernel of A? The primitive elements
of A? (Clearly, A can be recovered from S.)

I am just afraid that my description of the situation is
unnecessarily complicated!

A well-known example of this situation is the set
A={2,3,4,5,...}. In this case S consists of the prime
numbers.

Do you know of other nontrivial examples? By "trivial"
example I mean one in which the "prime kernel" is a
finite set.

Thanks,
Emeric

P.S. The sequence I have in mind is the sequence in
my May 16 posting: "a new sequence". The "prime
kernel" is 6,20,28,45,63,70,... .