deletable primes

[Ray Chandler]

> Phil Carmody recently submitted a(9) through a(13) of A125589.
> I disagree with him starting at a(10) though.
> 
> I also have more terms for A125590 but since the ones I found above
> disagree with the recent contribution of Phil Carmody, I will wait
> until someone (Phil or otherwise) checks to make sure my program is
> generating good numbers.  

I confirm Joshua's correction and extension of A125589 through a(18) and his extension of A125590 through a(15).

Ray Chandler





Consider the sequence {a(k)}, where:

a(1)=1. a(2) = 2.
For n>=3, a(n) is the smallest positive integer not occurring earlier in 
the sequence such that (sum{k=1 to n) a(k)) divides product{j=1 to n} 
a(j).

I calculate (by hand and by calculator) the sequence beginning:

1,2,3,6,4,8,12,18,10,...

I am about to submit this sequence, but I am unsure I didn't make an 
error.
(I bet I did make an error, because the sequence as written above has no 
hits in the OEIS.)

Is this sequence a permutation of the positive integers?


Thanks,
Leroy Quet