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.
This sequence is a permutation of the positive integers.
EXAMPLE
Triangle of strict partitions begins:
0
(1)
(2)
(3) (21)
(4) (31)
(5) (41) (32)
(6) (51) (42) (321)
(7) (61) (43) (52) (421)
(8) (71) (62) (53) (431) (521)
(9) (81) (72) (54) (63) (621) (531) (432).
MATHEMATICA
nn=25;
FDprimeList=Select[Range[nn], MatchQ[FactorInteger[#], {{_?PrimeQ, _?(MatchQ[FactorInteger[2#], {{2, _}}]&)}}]&];
Table[Sort[Times@@FDprimeList[[#]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, Length[FDprimeList]}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Feb 18 2018
STATUS
approved