[seqfan] Re: Q: A118663 prime(n) smallest prime factor of composite

israel at math.ubc.ca israel at math.ubc.ca
Tue Apr 3 20:18:40 CEST 2012

It seems that if m is the n'th composite (starting with 2), then A118663(n) 
= j where the j'th prime is the smallest prime factor of m. Thus 
A118663(21)=2 because the 21st composite is 33 and the smallest prime 
factor of 33 is 3, which is the second prime. However, there seem to be 
five errors in the given data:

A118663[23] should be 3 not 5 as the 23th composite is 35=(5)*(7)
A118663[53] should be 2 not 3 as the 53th composite is 75=(3)*(5)^2
A118663[66] should be 4 not 2 as the 66th composite is 91=(7)*(13)
A118663[77] should be 2 not 3 as the 77th composite is 105=(3)*(5)*(7)
A118663[102] should be 2 not 3 as the 102th composite is 135=(3)^3*(5)

Robert Israel
University of British Columbia

On Apr 3 2012, Richard Mathar wrote:

>Does someone understand how the terms of http://oeis.org/A118663
>relate to the definition?
>In my eyes, prime(n) is always the smallest prime factor of a composite
>number (?)
>Seqfan Mailing list - http://list.seqfan.eu/

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