[seqfan] Re: relation A091440 to A167348

drew at math.mit.edu drew at math.mit.edu
Thu Sep 3 21:23:36 CEST 2009

I think that A167438 is a duplicate of A091440.

The primorial p# is typically defined as the product of the primes less 
than or equal to p (here p is usually itself prime, but it need not be).

See http://primes.utm.edu/top20/page.php?id=5 for example.

Thus 1# = 1 (the empty product), phi(1#) = 1, and 1#/phi(1#) >= 1. This 
implies that A167348(1) should be 1.

The title of A091440 is slightly unfortunate in that it uses the words 
"smallest prime p", when "smallest integer p" would be more correct and 
agree with A091440(1)=1.



On Sep 3 2009, Richard Mathar wrote:

>I see that the sequences A091440 and A167348
>differ at n=1, because the PARI program in A167348 does not
>define primorials smaller than 2, wheras A091440 makes it
>very clear what its definition of primorials are. I cannot find
>the alternative where p# >= 2 in the OEIS. Does this mean 
>that A167348 is just an erroneous version of A091440? 
> http://research.att.com/~njas/sequences/?q=id:A167348|id:A091440 
> 2,2,3,7,13,23,43,79,149,257,461,821,1451,2549,4483,7879,13859,24247,42683,75037,131707,230773,405401,710569,1246379,2185021,3831913, 
> 1,2,3,7,13,23,43,79,149,257,461,821,1451,2549,4483,7879,13859,24247,42683,75037,131707,230773,405401,710569,1246379,2185021,3831913,6720059,11781551,20657677,36221753,63503639,111333529,195199289,
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