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A299759 Triangle read by rows in which row n lists in order all FDH numbers of strict integer partitions of n.

%I A299759 #11 Feb 23 2018 11:11:44
%S A299759 1,2,3,4,6,5,8,7,10,12,9,14,15,24,11,18,20,21,30,13,22,27,28,40,42,16,
%T A299759 26,33,35,36,54,56,60,17,32,39,44,45,66,70,72,84,120,19,34,48,52,55,
%U A299759 63,78,88,90,105,108,168,23,38,51,64,65,77,96,104,110,126
%N A299759 Triangle read by rows in which row n lists in order all FDH numbers of strict integer partitions of n.
%C A299759 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.
%C A299759 This sequence is a permutation of the positive integers.
%e A299759 Triangle of strict partitions begins:
%e A299759                   0
%e A299759                  (1)
%e A299759                  (2)
%e A299759                (3) (21)
%e A299759                (4) (31)
%e A299759              (5) (41) (32)
%e A299759           (6) (51) (42) (321)
%e A299759         (7) (61) (43) (52) (421)
%e A299759      (8) (71) (62) (53) (431) (521)
%e A299759 (9) (81) (72) (54) (63) (621) (531) (432).
%t A299759 nn=25;
%t A299759 FDprimeList=Select[Range[nn],MatchQ[FactorInteger[#],{{_?PrimeQ,_?(MatchQ[FactorInteger[2#],{{2,_}}]&)}}]&];
%t A299759 Table[Sort[Times@@FDprimeList[[#]]&/@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,Length[FDprimeList]}]
%Y A299759 Cf. A050376, A056239, A064547, A106400, A122111, A213925, A215366, A246867, A279065, A279614, A299755, A299757, A299758.
%Y A299759 Row lengths give A000009.
%K A299759 nonn,tabf
%O A299759 1,2
%A A299759 _Gus Wiseman_, Feb 18 2018