[seqfan] Re: Divisibility sequences in OEIS.
Henry in Rotherhithe
se16 at btinternet.com
Sat Dec 12 03:09:36 CET 2009
franktaw at netscape.net wrote:
> What is a divisibility sequence? Just glancing at examples doesn't
> tell me.
> There is no definition for divisibility sequence in either Mathworld or
> Wikipedia. (Wikipedia does have an entry for Elliptic Divisibility
> Sequence.) Does this term (without the elliptic) occur in the
> mathematical literature anywhere?
Morgan Ward, A note on divisibility sequences, Bull. Amer. Math. Soc.
Volume 45, Number 4 (1939), 334-336
suggests something like:
if k divides n then a(k) divides a(n)
This will cover a lot of sequences: constants, powers, factorials,
completely multiplicative functions and other multiplicative functions
where a(p^j) divides a(p^(j+1)), products of any of these, and many more
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