# [seqfan] Ratio-Related Sequence: Permutation Of +Integers?

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Wed May 6 23:48:13 CEST 2009

```I just submitted this (and A160257).

Is this sequence a permutation of the positive integers?
(By definition, no terms occurs more than once in the sequence. But does every term occur? I bet they do, but maybe the primes don't all necessarily occur.)

%I A160256
%S A160256 1,2,3,4,6,8,9,16,18,24,12,10,30,5,36,15,48
%N A160256 a(1)=1, a(2)=2. For n >=3, a(n) = the smallest positive integer not occurring earlier in the sequence such that a(n)*a(n-1)/a(n-2) is an integer.
%C A160256 Is this sequence a permutation of the positive integers?
%C A160256 a(n+2)*a(n+1)/a(n) = A160257(n).
%Y A160256 A075075,A160257
%K A160256 more,nonn
%O A160256 1,2

Also, in the related sequence A075075 (same as this sequence, except that the ratio a(n)*a(n-2)/a(n-1) is an integer), it states that that sequence is a permutation of the positive integers. Is this a fact?

Thanks,
Leroy Quet

```