[seqfan] a(n) divides the sum of the first n terms of T

[Eric Angelini]

Hello SeqFans,
I think T is not in the OEIS - and if so, I would need a little
help in computing it.

T is the lexically first sequence having no term repeated such
that a(n) divides the sum of the first n terms of T.

T = 1,3,2,5,9,7,8,13,15,11,14,16,26,24,41,29,18,28,...

T was extended using always the smallest integer not yet present
in T and not leading to a contradiction.

We see here that:

1 divides the sum 1
3 divides the sum of the first 3 terms [1+3+2=6]
2 divides the sum of the first 2 terms [1+3=4]
5 divides the sum of the first 5 terms [1+3+2+5+9=20]
9 divides the sum of the first 9 terms [1+3+2+5+9+7+8+13+15=63]
7 divides the sum of the first 7 terms [1+3+2+5+9+7+8=35]
8 divides the sum of the first 8 terms [1+3+2+5+9+7+8+13=48]
etc.

Let's use S for the cumulative sum of T's terms and n for n:

T= 1,3,2, 5, 9, 7, 8,13,15,11,14, 16, 26, 24, 41, 29, 18, 28,...
S= 1,4,6,11,20,27,35,48,63,74,88,104,130,154,195,224,242,270,...
n= 1 2 3  4  5  6  7  8  9 10 11  12  13  14  15  16  17  18 ...
          -     -          --     --                  --
When n doesn't divide S, we have a term not in T (underlined).

Best,
É.