A299758 - OEIS

%I #5 Feb 23 2018 11:11:38

%S 1,2,3,6,8,12,24,30,42,60,120,168,216,280,420,840,1080,1512,1890,2520,

%T 3780,7560,9240,11880,16632,20790,27720,41580,83160,98280,120960,

%U 154440,216216,270270,360360,540540,1081080,1330560,1572480,1921920,2471040,3459456,4324320

%N Largest FDH number of a strict integer partition of 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 realizing each maximum begins: () (1) (2) (21) (31) (32) (321) (421) (521) (432) (4321) (5321) (6321) (5431) (5432) (54321) (64321) (65321) (65421) (65431) (65432).

%t nn=150;

%t FDprimeList=Select[Range[nn],MatchQ[FactorInteger[#],{{_?PrimeQ,_?(MatchQ[FactorInteger[2#],{{2,_}}]&)}}]&];

%t Table[Max[Times@@FDprimeList[[#]]&/@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,Length[FDprimeList]}]

%Y Cf. A005518, A050376, A064547, A213925, A279065, A299755, A299757, A299759.

%K nonn

%O 1,2

%A _Gus Wiseman_, Feb 18 2018