[seqfan] Re: mth squarefree = mth prime power

Peter Pein petsie at dordos.net
Thu May 21 13:23:21 CEST 2009

Richard Mathar schrieb:
> lq> Leroy Quet q1qq2qqq3qqqq at yahoo.com
> lq> Sat May 16 18:45:48 CEST 2009
> lq> 
> lq> I just sent in this sequence. Is it complete?
> lq> 
> lq> %I A160513
> lq> %S A160513 1,2,3,7,17,19
> lq> %N A160513 Positive squarefree integers n such that, if n is the mth squarefree integer, then n is the mth power of a prime as well. 
> lq> %C A160513 Is this sequence complete? 
> lq> %C A160513 1 here is considered to be both the first squarefree integer and the first power of a prime. 
> lq> %Y A160513 A000961,A005117 
> lq> %K A160513 fini,more,nonn
> lq> %O A160513 1,2
> lq> 
> lq> 
> lq> Since the squarefree integers have a density of 6/pi^2; and since the density, as n approaches infinity, of the number of prime powers <= n approaches 0 (right?), then it is certain that this sequence is finite.
> lq> (Unless I am missing something here.)
Sorry, I don't get it...
Say m=2; then the second squarefree number shall be a second power of a prime???
Enlighten me please!

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