A045780 Least value with A045779(n) factorizations into distinct factors.

1, 6, 12, 64, 24, 256, 48, 512, 60, 96, 2048, 144, 210, 120, 216, 180, 384, 288, 16384, 240, 432, 420, 65536, 1536, 360, 480, 900, 864, 3072, 1152, 1296, 2310, 524288, 6144, 960, 720, 840, 2304, 1728, 1080, 1260, 2592, 2097152, 1800, 4608, 24576, 4194304, 1440, 3456

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..953

Example

From Gus Wiseman, Jan 11 2020: (Start)
The strict factorizations of a(n) for n = 1..9:
  ()  (6)    (12)   (64)     (24)     (256)     (48)     (512)     (60)
      (2*3)  (2*6)  (2*32)   (3*8)    (4*64)    (6*8)    (8*64)    (2*30)
             (3*4)  (4*16)   (4*6)    (8*32)    (2*24)   (16*32)   (3*20)
                    (2*4*8)  (2*12)   (2*128)   (3*16)   (2*256)   (4*15)
                             (2*3*4)  (2*4*32)  (4*12)   (4*128)   (5*12)
                                      (2*8*16)  (2*3*8)  (2*4*64)  (6*10)
                                                (2*4*6)  (2*8*32)  (2*5*6)
                                                         (4*8*16)  (3*4*5)
                                                                   (2*3*10)
(End)
30 is not in the sequence even though A045779(30) = 5. As 24 is the smallest k such that A045779(k) = 5 we have a(m) = 24 where m is such that A045779(m) = 5 which turns out to be m = 5 (not every positive integer is in A045779). So a(5) = 24. - David A. Corneth, Oct 24 2024

Crossrefs

All terms belong to A025487.

The non-strict version is A045783.

The sorted version is A330997.

Factorizations are A001055 with image A045782 and complement A330976.

Strict factorizations are A045778 with image A045779 and complement A330975.

The least number with exactly n strict factorizations is A330974(n).

Cf. A033833, A318286, A330972, A330973, A330989.

Sequence in context: A121735 A070970 A330974 * A088726 A163342 A107904

Adjacent sequences: A045777 A045778 A045779 * A045781 A045782 A045783

Keyword

nonn

Author

David W. Wilson

Extensions

More terms from David A. Corneth, Oct 24 2024

Status

approved