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 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).
MATHEMATICA
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)]]]]];
nn=200; FDprimeList=Array[FDfactor, nn, 1, Union];
FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Join@@Table[Reverse[FDfactor[n]/.FDrules], {n, nn}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Feb 18 2018
STATUS
approved