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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