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a(1) = 1, and for n > 1, a(n) is the greatest k > 0 such that (a(1), ..., a(n-1)) can be split into k chunks of contiguous terms and those chunks have the same sum.
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%I #12 Jun 25 2019 01:40:15

%S 1,1,2,2,3,1,1,1,2,1,1,1,1,3,1,2,4,2,5,1,6,7,1,1,1,1,1,3,1,1,1,2,1,3,

%T 1,1,1,1,2,4,1,1,1,1,1,1,1,1,4,1,1,5,1,1,1,2,2,2,2,2,6,2,2,2,4,2,7,1,

%U 2,2,2,2,1,1,8,2,2,3,3,9,3,3,3,10,2,2,2

%N a(1) = 1, and for n > 1, a(n) is the greatest k > 0 such that (a(1), ..., a(n-1)) can be split into k chunks of contiguous terms and those chunks have the same sum.

%C For any n > 0, a(n) divides Sum_{k = 1..n-1} a(k).

%C Is this sequence unbounded?

%H Rémy Sigrist, <a href="/A308746/b308746.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A308746/a308746.png">Colored scatterplot of the first 1000000 terms</a> (where the color is function of Sum_{k = 1..n-1} a(k) / a(n))

%H Rémy Sigrist, <a href="/A308746/a308746.gp.txt">PARI program for A308746</a>

%e The first terms, alongside the corresponding chunks, are:

%e n a(n) Chunks (separated by pipes)

%e -- ---- -------------------------------------

%e 1 1

%e 2 1 1

%e 3 2 1|1

%e 4 2 1 1|2

%e 5 3 1 1|2|2

%e 6 1 1 1 2 2 3

%e 7 1 1 1 2 2 3 1

%e 8 1 1 1 2 2 3 1 1

%e 9 2 1 1 2 2|3 1 1 1

%e 10 1 1 1 2 2 3 1 1 1 2

%e 11 1 1 1 2 2 3 1 1 1 2 1

%e 12 1 1 1 2 2 3 1 1 1 2 1 1

%e 13 1 1 1 2 2 3 1 1 1 2 1 1 1

%e 14 3 1 1 2 2|3 1 1 1|2 1 1 1 1

%e 15 1 1 1 2 2 3 1 1 1 2 1 1 1 1 3

%e 16 2 1 1 2 2 3 1 1|1 2 1 1 1 1 3 1

%e 17 4 1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2

%e 18 2 1 1 2 2 3 1 1 1 2|1 1 1 1 3 1 2 4

%e 19 5 1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2|4 2

%e 20 1 1 1 2 2 3 1 1 1 2 1 1 1 1 3 1 2 4 2 5

%o (PARI) See Links section.

%Y Cf. A095258.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Jun 21 2019