OFFSET
0,14
COMMENTS
An integer partition has unsortable prime factors if there is no permutation (c_1,...,c_k) of the parts such that the maximum prime factor of c_i is at most the minimum prime factor of c_{i+1}. For example, the partition (27,8,6) is sortable because the permutation (8,6,27) satisfies the condition.
EXAMPLE
The a(12) = 1 through a(17) = 14 partitions:
(6,6) (10,3) (6,6,2) (6,6,3) (10,6) (14,3)
(6,6,1) (10,3,1) (10,3,2) (6,6,4) (6,6,5)
(6,6,1,1) (6,6,2,1) (10,3,3) (10,4,3)
(10,3,1,1) (6,6,2,2) (10,6,1)
(6,6,1,1,1) (6,6,3,1) (6,6,3,2)
(10,3,2,1) (6,6,4,1)
(6,6,2,1,1) (10,3,2,2)
(10,3,1,1,1) (10,3,3,1)
(6,6,1,1,1,1) (6,6,2,2,1)
(6,6,3,1,1)
(10,3,2,1,1)
(6,6,2,1,1,1)
(10,3,1,1,1,1)
(6,6,1,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !OrderedQ[Join@@Sort[First/@FactorInteger[#]&/@#, OrderedQ[PadRight[{#1, #2}]]&]]&]], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 27 2019
STATUS
approved