Observation on A053669

[David Wilson]

Another possible description of A053669:

Smallest prime non-divisor of n.

----- Original Message ----- 
From: "Richard Mathar" <mathar at strw.leidenuniv.nl>
To: <seqfan at ext.jussieu.fr>
Sent: Saturday, November 04, 2006 3:45 PM
Subject: Re: Observation on A053669


>
> dww> From seqfan-owner at ext.jussieu.fr  Sat Nov  4 21:12:32 2006
> dww> Return-Path: <seqfan-owner at ext.jussieu.fr>
> dww> From: "David Wilson" <davidwwilson at comcast.net>
> dww> To: "Sequence Fans" <seqfan at ext.jussieu.fr>
> dww> Subject: Observation on A053669
> dww> ...
> dww> It seems to me that
> dww>
> dww> %N A053669 Smallest prime co-prime to n.
> dww>
> dww> could just as easily be described
> dww>
> dww> %N A053669 Smallest number > 1 coprime to n.
> dww>
> dww> and the fact that a(n) is prime falls out.  This definition would 
> also =
> dww> simplify the program.
> dww>...
>
> Yes. If the smallest prime co-prime to n would not be a prime,
> it would be built by at least two prime factors, the smaller of which
> would be the correct entry (proof by reductio ad absurdum).
>
> It would still be useful to keep in a comment that the numbers are all 
> prime
> (this might speed up some searches for the numbers...)
>
> I'd propose to list in a comment the first occurrences of the first 
> primes:
> first 5 at a(6)
> first 7 is a(30)
> first 11 is a(210)
> first 13 is a(2310)
> first 17 is a(30030)
> first 19 is a(510510)
> where the indices are 6=2*3, 30=2*3*5, 210=2*3*5*7, 2*3*5*7*11 etc,
> (the primorials, I guess, as in A002110)
>
> -- RJM
>
>
> -- 
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