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.

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, 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, 2, 2, 2, 2, 1, 1, 8, 2, 2, 3, 3, 9, 3, 3, 3, 10, 2, 2, 2

Offset: 1

Author

Rémy Sigrist, Jun 21 2019

Keywords

• nonn

Comments

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

Is this sequence unbounded?

Examples

			The first terms, alongside the corresponding chunks, are:
  n   a(n)  Chunks (separated by pipes)
  --  ----  -------------------------------------
   1     1
   2     1  1
   3     2  1|1
   4     2  1 1|2
   5     3  1 1|2|2
   6     1  1 1 2 2 3
   7     1  1 1 2 2 3 1
   8     1  1 1 2 2 3 1 1
   9     2  1 1 2 2|3 1 1 1
  10     1  1 1 2 2 3 1 1 1 2
  11     1  1 1 2 2 3 1 1 1 2 1
  12     1  1 1 2 2 3 1 1 1 2 1 1
  13     1  1 1 2 2 3 1 1 1 2 1 1 1
  14     3  1 1 2 2|3 1 1 1|2 1 1 1 1
  15     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3
  16     2  1 1 2 2 3 1 1|1 2 1 1 1 1 3 1
  17     4  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2
  18     2  1 1 2 2 3 1 1 1 2|1 1 1 1 3 1 2 4
  19     5  1 1 2 2|3 1 1 1|2 1 1 1 1|3 1 2|4 2
  20     1  1 1 2 2 3 1 1 1 2 1 1 1 1 3 1 2 4 2 5
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 1000000 terms (where the color is function of Sum_{k = 1..n-1} a(k) / a(n))
• Rémy Sigrist, PARI program for A308746

Crossrefs

Cf. A095258.

Programs

PARI

See Links section.