A299759 Triangle read by rows in which row n lists in order all FDH numbers of strict integer partitions of n.

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

Offset: 1

Author

Gus Wiseman, Feb 18 2018

Keywords

• nonn
• tabf

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.

Examples

			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).
		

Crossrefs

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

Row lengths give A000009.

Programs

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]}]