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A299758 Largest FDH number of a strict integer partition of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 23 06:58 EDT 2019. Contains 328335 sequences. (Running on oeis4.)