OFFSET
0,6
EXAMPLE
The partition (10,6,4) has choice (5,3,2) so is counted under a(20).
The a(0) = 1 through a(10) = 4 partitions:
() . (2) (3) (4) (5) (6) (7) (8) (9) (10)
(3,2) (4,3) (5,3) (5,4) (6,4)
(5,2) (6,2) (6,3) (7,3)
(7,2) (5,3,2)
The a(0) = 1 through a(17) = 12 partitions (0 = {}, A..H = 10..17):
0 . 2 3 4 5 6 7 8 9 A B C D E F G H
32 43 53 54 64 65 66 76 86 87 97 98
52 62 63 73 74 75 85 95 96 A6 A7
72 532 83 A2 94 A4 A5 B5 B6
92 543 A3 B3 B4 C4 C5
732 B2 C2 C3 D3 D4
652 653 D2 E2 E3
743 654 754 F2
752 753 763 665
762 853 764
A32 952 A43
B32 7532
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 29 2024
STATUS
approved