[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

Henry Bottomley

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