OFFSET
1,2
COMMENTS
Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive integer n has a unique factorization of the form n = f(s_1)*...*f(s_k) where the s_i are strictly increasing positive integers. This determines a unique strict integer partition (s_k...s_1) whose FDH number is then defined to be n.
EXAMPLE
Sequence of strict integer partitions realizing each maximum begins: () (1) (2) (21) (31) (32) (321) (421) (521) (432) (4321) (5321) (6321) (5431) (5432) (54321) (64321) (65321) (65421) (65431) (65432).
MATHEMATICA
nn=150;
FDprimeList=Select[Range[nn], MatchQ[FactorInteger[#], {{_?PrimeQ, _?(MatchQ[FactorInteger[2#], {{2, _}}]&)}}]&];
Table[Max[Times@@FDprimeList[[#]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, Length[FDprimeList]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 18 2018
STATUS
approved