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

Maximilian Hasler maximilian.hasler at gmail.com
Tue Apr 3 20:35:43 CEST 2012

I agree with your suggestion: the PARI code

for(i=2,999,isprime(i)&next;print1(primepi(factor(i)[1,1])","))

reproduces the sequence up to the errors you found.
I renamed the sequence to
"
Index of the least prime dividing the n-th composite number:
A000720(A020639(A002808(n))).
"

Maximilian

On Tue, Apr 3, 2012 at 2:18 PM,  <israel at math.ubc.ca> wrote:
> 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 should be 3 not 5 as the 23th composite is 35=(5)*(7)
> A118663 should be 2 not 3 as the 53th composite is 75=(3)*(5)^2
> A118663 should be 4 not 2 as the 66th composite is 91=(7)*(13)
> A118663 should be 2 not 3 as the 77th composite is 105=(3)*(5)*(7)
> A118663 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 (?)
>>
>> RJM
>>
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