OFFSET
0,3
EXAMPLE
For the partitions of 5 we have the following choices:
(5): {{1},{5}}
(41): {{1,1},{1,2},{1,4}}
(32): {{1,1},{1,2},{1,3},{2,3}}
(311): {{1,1,1},{1,1,3}}
(221): {{1,1,1},{1,1,2},{1,2,2}}
(2111): {{1,1,1,1},{1,1,1,2}}
(11111): {{1,1,1,1,1}}
So a(5) = 4.
MATHEMATICA
Table[Max[Length[Union[Sort/@Tuples[Divisors/@#]]]&/@IntegerPartitions[n]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 05 2024
EXTENSIONS
Terms a(31) onward from Max Alekseyev, Sep 17 2024
STATUS
approved