A299758 Largest 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

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.

Links

Table of n, a(n) for n=1..43.

Example

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).

Mathematica

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]}]

Crossrefs

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

Sequence in context: A270738 A049194 A058298 * A303703 A101136 A036957

Adjacent sequences: A299755 A299756 A299757 * A299759 A299760 A299761

Keyword

nonn

Author

Gus Wiseman, Feb 18 2018

Status

approved