# primes less than n and relatively prime to n

Hans Havermann pxp at rogers.com
Fri Jan 19 22:54:47 CET 2007

```I don't see in OEIS [n/2] + [n/3] + [n/5].
which if I've done this right by hand begins for n = 1,2,3,...:
0, 1, 2, 3, 4, 6, 6, 7, 7, 10, 10, 12, 12, 13, 15, 16, 16, 18, 18, 20, ...

There are an infinite number of such sequences.  This is vaguely
related to A008615 [n/2] - [n/4].

I can't tell is this is artificial, or an interesting part of the
supersequence which also includes, for instance:

2 | [n/2] + [n/3]
3 | [n/2] + [n/3] + [n/5]
4 | [n/2] + [n/3] + [n/5] + [n/7]
5 | [n/2] + [n/3] + [n/5] + [n/7] + [n/11]
6 | [n/2] + [n/3] + [n/5] + [n/7] + [n/11] + [n/13]

Doesn't this seem like an awful lot of very random messages to a
large list in order resolve what seems to be a very small confusion?

I apologize I don't have time to carefully thread through all the
nearly indecipherable postings trying to decode mysteries like what
"A....." refers to, "proofs" without a clear statement of any
theorem, critiques of documentation for programming languages,
etc--so I might have missed something.

Nonetheless from just a cursory reading it seems clear--since SOME
primes less than n are NOT relatively prime to n (for example p=5,
n=100)--the qualifying clause in the subject line should be a
perfectly reasonable and necessary condition for a sequence.

Don't you think that simply the number of times it appears in the
OEIS *might* indicate that it's saying something legitimate, whose
meaning might be extracted with just a little mental effort?

Maybe there needs to be a separate discussion group or something for
this kind of traffic?  Or else maybe we could exercise a bit more
restraint and/or engage in more 1-on-1 communications and/or simply
invest more thought before sending mail?

I'm usually content to simply delete these kinds of messages, but I'm
beginning to see why that overhead might be driving people
away.  Please, folks, let's do better.

Thanks!

(PS Apologies also if these suggestions have already been discussed
to death--I probably deleted those threads too!<;-)

```