asking help in terminology

[franktaw at netscape.net]

The primitive abundant numbers are A091191.
 
The composite numbers A002808 have the semiprimes A001358 as primitive elements; there is a comment to this effect.
 
For A009003, the primitive elements are A002144.
 
I would argue against describing this simply as the "kernel" of the sequence.  There are too many kernels of different types floating around already.  "Multiplicative kernel" would be better.  But really, I don't see any problem with saying "primitive elements of" the sequence.  It has the singular advantage that it is already in use.
 
Franklin T. Adams-Watters
 
 
-----Original Message-----
From: 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,... .
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