OFFSET
0,5
COMMENTS
For example, the only choice for the partition (9,9,6,6,6) is {1,2,3,6,9}.
EXAMPLE
The a(1) = 1 through a(15) = 13 partitions (A = 10, B = 11, C = 12, D = 13):
1 . 21 22 . 33 322 71 441 55 533 B1 553 77 933
31 51 421 332 522 442 722 444 733 D1 B22
321 422 531 721 731 552 751 B21 B31
521 4321 4322 4332 931 4433 4443
5321 4431 4432 5441 5442
5322 5332 6332 5532
5421 5422 7322 6621
6321 6322 7421 7332
7321 7422
7521
8421
9321
54321
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Length[Union[Sort /@ Select[Tuples[Divisors/@#], UnsameQ@@#&]]]==1&]], {n, 0, 30}]
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 03 2024
STATUS
approved