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%I #12 Feb 23 2018 11:11:19
%S 1,2,3,4,2,1,5,3,1,6,4,1,7,3,2,8,5,1,4,2,9,10,6,1,11,4,3,5,2,7,1,12,3,
%T 2,1,13,8,1,6,2,5,3,14,4,2,1,15,9,1,7,2,10,1,5,4,6,3,16,11,1,8,2,4,3,
%U 1,17,5,2,1,18,7,3,6,4,12,1,19,9,2,20,13,1
%N Triangle read by rows in which row n is the strict integer partition with FDH number n.
%C 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.
%e Sequence of strict integer partitions begins: () (1) (2) (3) (4) (2,1) (5) (3,1) (6) (4,1) (7) (3,2) (8) (5,1) (4,2) (9) (10) (6,1) (11) (4,3) (5,2) (7,1) (12) (3,2,1) (13) (8,1) (6,2) (5,3) (14) (4,2,1) (15).
%t FDfactor[n_]:=If[n===1,{},Sort[Join@@Cases[FactorInteger[n],{p_,k_}:>Power[p,Cases[Position[IntegerDigits[k,2]//Reverse,1],{m_}->2^(m-1)]]]]];
%t nn=200;FDprimeList=Array[FDfactor,nn,1,Union];
%t FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];
%t Join@@Table[Reverse[FDfactor[n]/.FDrules],{n,nn}]
%Y Row lengths are A064547.
%Y Cf. A005117, A050376, A112798, A213925, A246867, A296150, A299756, A299757, A299759.
%K nonn,tabf
%O 1,2
%A _Gus Wiseman_, Feb 18 2018
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