[seqfan] Re: Divisibility sequences in OEIS.

Creighton Kenneth Dement creighton.k.dement at mail.uni-oldenburg.de
Sat Dec 12 12:45:59 CET 2009

> Morgan Ward, A note on divisibility sequences, Bull. Amer. Math. Soc.
> Volume 45, Number 4 (1939), 334-336
> http://www.ams.org/bull/1936-42-12/S0002-9904-1936-06435-9/S0002-9904-1936-06435-9.pdf
> 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

I believe many of these sequences also share a similar divisibilty property:
For m > n, if k divides a(m) and a(n), then k divides a(2*m-n).

See comments for A105963, A105951.


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