A319825 - OEIS

%I #5 Sep 29 2018 12:57:42

%S 0,1,2,3,4,2,5,3,6,4,7,6,8,5,4,9,10,6,11,12,10,7,12,6,13,8,6,15,14,4,

%T 15,9,14,10,20,6,16,11,8,12,17,10,18,21,12,12,19,18,20,13,10,24,21,6,

%U 28,15,22,14,22,12,23,15,30,9,8,14,24,30,12,20,25,6,26

%N LCM of the strict integer partition with FDH number n.

%C Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1, ..., y_k) is f(y_1) * ... * f(y_k).

%e 45 is the FDH number of (6,4), which has LCM 12, so a(45) = 12.

%t nn=200;

%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 FDprimeList=Array[FDfactor,nn,1,Union];FDrules=MapIndexed[(#1->#2[[1]])&,FDprimeList];

%t LCM@@@Table[Reverse[FDfactor[n]/.FDrules],{n,2,nn}]

%Y Cf. A050376, A056239, A064547, A213925, A289508, A289509, A290103, A299755, A299757, A319826.

%K nonn

%O 1,3

%A _Gus Wiseman_, Sep 28 2018