(a(1)+a(2)+..a(n)) divides a(1)*a(2)*..a(n)

[Leroy Quet]

> 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?
> 

I agree with your calculations.  First 102 terms follow:

{1, 2, 3, 6, 4, 8, 12, 18, 10, 16, 20, 25, 19, 27, 9, 36, 24, 30, 15, 35, 22, \
33, 5, 38, 14, 43, 11, 26, 13, 7, 28, 34, 31, 21, 17, 23, 29, 39, 44, 42, 40, \
32, 45, 51, 37, 47, 48, 50, 52, 46, 56, 60, 41, 55, 54, 58, 53, 57, 49, 62, \
59, 61, 63, 64, 65, 69, 66, 70, 68, 73, 71, 77, 67, 78, 72, 84, 75, 79, 74, \
80, 82, 86, 88, 87, 81, 85, 83, 93, 92, 89, 91, 95, 94, 90, 76, 101, 96, 103, \
98, 102, 99, 97}

First term missing is 100.

First term missing from first 1002 terms is 998.  

Ray Chandler