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A299759 Triangle read by rows in which row n lists in order all FDH numbers of strict integer partitions of n. 7
1, 2, 3, 4, 6, 5, 8, 7, 10, 12, 9, 14, 15, 24, 11, 18, 20, 21, 30, 13, 22, 27, 28, 40, 42, 16, 26, 33, 35, 36, 54, 56, 60, 17, 32, 39, 44, 45, 66, 70, 72, 84, 120, 19, 34, 48, 52, 55, 63, 78, 88, 90, 105, 108, 168, 23, 38, 51, 64, 65, 77, 96, 104, 110, 126 (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.

This sequence is a permutation of the positive integers.

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

Triangle of strict partitions begins:

                  0

                 (1)

                 (2)

               (3) (21)

               (4) (31)

             (5) (41) (32)

          (6) (51) (42) (321)

        (7) (61) (43) (52) (421)

     (8) (71) (62) (53) (431) (521)

(9) (81) (72) (54) (63) (621) (531) (432).

MATHEMATICA

nn=25;

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

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

CROSSREFS

Cf. A050376, A056239, A064547, A106400, A122111, A213925, A215366, A246867, A279065, A279614, A299755, A299757, A299758.

Row lengths give A000009.

Sequence in context: A260307 A285041 A265734 * A232560 A183090 A232559

Adjacent sequences:  A299756 A299757 A299758 * A299760 A299761 A299762

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Feb 18 2018

STATUS

approved

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Last modified October 17 16:51 EDT 2019. Contains 328120 sequences. (Running on oeis4.)