# [seqfan] Re: multiplicative set-like sequences

franktaw at netscape.net franktaw at netscape.net
Sat Feb 26 15:25:00 CET 2011

```I agree with Juan.

First of all, I suspect the concept is actually:

if gcd(m,n) = 1, then mn is in the sequence if and only if m and n both
are.

If this is correct, it is equivalent to the condition that the
characteristic function of the sequence is multiplicative.

If the condition as stated is actually what is intended, then these
certainly should not be called multiplicative.

-----Original Message-----
From: Juan Arias de Reyna <arias at us.es>

I speak as a  user of OEIS:

The concept of multiplicative sequence is found in almost any
elementary book on Number Theory: (a_n) is multiplicative  if
gcd(n,m)=1 implies  a_{nm}=a_n a_m.

I consider that this other concept must be clearly separated
from that now proposed:

> "mn in the the sequence if m,n are in the sequence and g.c.d.(m,n)=1"

Call it as set multiplicative sequences or something similar and
consider
a new keyword.  (I suggest set-mult )

The same word for two different meanings is surely a bad election.

Best regards,
Juan Arias de Reyna

El 26/02/2011, a las 08:46, Max Alekseyev escribió:

> Neil,
>
> To avoid confusion, we need then to extended the definition of the
> 'mult' keyword given at http://oeis.org/eishelp2.html#RK
> with
> "mn in the the sequence if m,n are in the sequence and g.c.d.(m,n)=1"
>
> or maybe introduce a new keyword like "mult2" (I'm still not sure if
> it is a good idea to have two distinct definitions for the same
> keyword).
>
> Regards,
> Max
>
> On Wed, Feb 16, 2011 at 8:06 PM, N. J. A. Sloane
<njas at research.att.com>
wrote:
>>> Should such set-like sequences are also marked with the 'mult'
keyword?
>> A typical candidate would be A023172.
>>
>> My answer is Yes, certainly!
>> Neil

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