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proposed

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive n 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.

allocated for Gus WisemanLargest FDH number of a strict integer partition of n.

1, 2, 3, 6, 8, 12, 24, 30, 42, 60, 120, 168, 216, 280, 420, 840, 1080, 1512, 1890, 2520, 3780, 7560, 9240, 11880, 16632, 20790, 27720, 41580, 83160, 98280, 120960, 154440, 216216, 270270, 360360, 540540, 1081080, 1330560, 1572480, 1921920, 2471040, 3459456, 4324320

1,2

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. Every positive n integer 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.

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).

nn=150;

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

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

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

allocated

nonn

Gus Wiseman, Feb 18 2018

approved

editing

allocated for Gus Wiseman

allocated

approved