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A308746 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.

%I A308746 #12 Jun 25 2019 01:40:15
%S A308746 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 A308746 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 A308746 2,2,2,2,1,1,8,2,2,3,3,9,3,3,3,10,2,2,2
%N A308746 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 A308746 For any n > 0, a(n) divides Sum_{k = 1..n-1} a(k).
%C A308746 Is this sequence unbounded?
%H A308746 Rémy Sigrist, <a href="/A308746/b308746.txt">Table of n, a(n) for n = 1..10000</a>
%H A308746 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 A308746 Rémy Sigrist, <a href="/A308746/a308746.gp.txt">PARI program for A308746</a>
%e A308746 The first terms, alongside the corresponding chunks, are:
%e A308746   n   a(n)  Chunks (separated by pipes)
%e A308746   --  ----  -------------------------------------
%e A308746    1     1
%e A308746    2     1  1
%e A308746    3     2  1|1
%e A308746    4     2  1 1|2
%e A308746    5     3  1 1|2|2
%e A308746    6     1  1 1 2 2 3
%e A308746    7     1  1 1 2 2 3 1
%e A308746    8     1  1 1 2 2 3 1 1
%e A308746    9     2  1 1 2 2|3 1 1 1
%e A308746   10     1  1 1 2 2 3 1 1 1 2
%e A308746   11     1  1 1 2 2 3 1 1 1 2 1
%e A308746   12     1  1 1 2 2 3 1 1 1 2 1 1
%e A308746   13     1  1 1 2 2 3 1 1 1 2 1 1 1
%e A308746   14     3  1 1 2 2|3 1 1 1|2 1 1 1 1
%e A308746   15     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3
%e A308746   16     2  1 1 2 2 3 1 1|1 2 1 1 1 1 3 1
%e A308746   17     4  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2
%e A308746   18     2  1 1 2 2 3 1 1 1 2|1 1 1 1 3 1 2 4
%e A308746   19     5  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2|4 2
%e A308746   20     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3 1 2 4 2 5
%o A308746 (PARI) See Links section.
%Y A308746 Cf. A095258.
%K A308746 nonn
%O A308746 1,3
%A A308746 _Rémy Sigrist_, Jun 21 2019