A045783 Least value with A045782(n) factorizations.

1, 4, 8, 12, 16, 24, 36, 60, 48, 128, 72, 96, 120, 256, 180, 144, 192, 216, 420, 240, 1024, 384, 288, 360, 2048, 432, 480, 900, 768, 840, 576, 1260, 864, 720, 8192, 960, 1080, 1152, 4620, 1800, 3072, 1680, 1728, 1920, 1440, 32768, 2304, 2592, 6144

Offset

1,2

Links

Table of n, a(n) for n=1..49.

Wikipedia, Multiplicative partition

R. E. Canfield, P. Erdős and C. Pomerance, On a Problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory 17 (1983), 1-28.

Example

From Gus Wiseman, Jan 11 2020: (Start)
Factorizations of n = 1, 4, 8, 12, 16, 24, 36, 60, 48:
  {}  4    8      12     16       24       36       60       48
      2*2  2*4    2*6    2*8      3*8      4*9      2*30     6*8
           2*2*2  3*4    4*4      4*6      6*6      3*20     2*24
                  2*2*3  2*2*4    2*12     2*18     4*15     3*16
                         2*2*2*2  2*2*6    3*12     5*12     4*12
                                  2*3*4    2*2*9    6*10     2*3*8
                                  2*2*2*3  2*3*6    2*5*6    2*4*6
                                           3*3*4    3*4*5    3*4*4
                                           2*2*3*3  2*2*15   2*2*12
                                                    2*3*10   2*2*2*6
                                                    2*2*3*5  2*2*3*4
                                                             2*2*2*2*3
(End)

Crossrefs

All terms belong to A025487.

The strict version is A045780.

The sorted version is A330972.

Includes all highly factorable numbers A033833.

The least number with exactly n factorizations is A330973(n).

Factorizations are A001055 with image A045782 and complement A330976.

Strict factorizations are A045778 with image A045779 and complement A330975.

Cf. A070175, A318284, A325238, A330974, A330989, A330992, A330998.

Sequence in context: A033833 A291834 A291928 * A316712 A261650 A178731

Adjacent sequences: A045780 A045781 A045782 * A045784 A045785 A045786

Keyword

nonn

Author

David W. Wilson

Status

approved