[seqfan] mth squarefree = mth prime power

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Sat May 16 18:45:48 CEST 2009

I just sent in this sequence. Is it complete?

%I A160513
%S A160513 1,2,3,7,17,19
%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. 
%C A160513 Is this sequence complete? 
%C A160513 1 here is considered to be both the first squarefree integer and the first power of a prime. 
%Y A160513 A000961,A005117 
%K A160513 fini,more,nonn
%O A160513 1,2

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.
(Unless I am missing something here.)

Leroy Quet


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