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

Author

David W. Wilson

Keywords

• nonn

Examples

			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
		

Links

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

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.

Extensions

More terms from David A. Corneth, Oct 24 2024