Divisors Of Sum Of Previous Rows

[Leroy Quet]

I just submitted these sequences:

>%S A120576 2,1,3,6,4,12,7,14,28,11,77
>%N A120576 Irregular array where the nth row are the divisors, not 
>occurring earlier in the sequence, of the sum of the terms in all previous 
>rows. a(1)=2.
>%C A120576 Is this sequence a permutation of the positive integers?
>%e A120576 Array begins:
>2
>1
>3
>6
>4,12
>7,14,28
>Now these terms add up to 77. So row 7 is the divisors of 77 which don't 
>occur earlier in the sequence. 1 and 7 occur in earlier rows, so row 7 is 
>(11,77).
>%Y A120576 A120577,A120578,A120579
>%O A120576 1
>%K A120576 ,more,nonn,

>%S A120577 3,1,2,4,50,10,25,50,20,100
>%N A120577 Irregular array where the nth row are the divisors, not 
>occurring earlier in the sequence, of the sum of the terms in all previous 
>rows. a(1)=3.
>%C A120577 Is this sequence a permutation of the positive integers?
>%e A120577 Array begins:
>3
>1
>2,4
>5,10
>25
>50
>Now these terms add up to 100. So row 7 is the divisors of 100 which don't 
>occur earlier in the sequence. 1,2,4,5,10,25, and 50 occur in earlier 
>rows, so row 7 is (20,100).
>%Y A120577 A120576,A120578,A120579
>%O A120577 1
>%K A120577 ,more,nonn,

>%S A120578 4,1,2,7,14,28,8,56,3,5,6,10,12,15,20,24,30,40,60,120
>%N A120578 Irregular array where the nth row are the divisors, not 
>occurring earlier in the sequence, of the sum of the terms in all previous 
>rows. a(1)=4.
>%C A120578 Is this sequence a permutation of the positive integers?
>%e A120578 Array begins:
>4
>1,2
>7
>14
>28
>8,56
>Now these terms add up to 120. So row 7 is the divisors of 120 which don't 
>occur earlier in the sequence. 1,2,4, and 8 occur in earlier rows, so row 
>7 is (3,5,6,10,12,15,20,24,30,40,60,120).
>%Y A120578 A120576,A120577,A120579
>%O A120578 1
>%K A120578 ,more,nonn,

(I also submitted the beginning of the sequence for a(1) = 5, but you get 
the idea.)




Question: Are the sequences generated this way each a permutation of the 
positive integers for a(1) = any integer >= 2?

If some a(1)'s lead to permutations and some do not, what would the 
sequence be of the a(1)'s which do (or don't) lead to permutations?

thanks,
Leroy Quet