asking help in terminology

[hv at crypt.org]

A23196 (non-deficient numbers) is another example, which has A6039
("primitive" non-deficient numbers) as its kernel.

A5101 (abundant numbers) also qualifies; its kernel does not appear
to be in OEIS.

Hugo

Emeric Deutsch <deutsch at duke.poly.edu> wrote:
: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,... .