A330989 Least positive integer with exactly 2^n factorizations into factors > 1, or 0 if no such integer exists.

1, 4, 12, 0, 72, 0, 480

Offset

0,2

Links

Table of n, a(n) for n=0..6.

Example

The A001055(n) factorizations for n = 1, 4, 12, 72:
  ()  (4)    (12)     (72)
      (2*2)  (2*6)    (8*9)
             (3*4)    (2*36)
             (2*2*3)  (3*24)
                      (4*18)
                      (6*12)
                      (2*4*9)
                      (2*6*6)
                      (3*3*8)
                      (3*4*6)
                      (2*2*18)
                      (2*3*12)
                      (2*2*2*9)
                      (2*2*3*6)
                      (2*3*3*4)
                      (2*2*2*3*3)

Crossrefs

All nonzero terms belong to A025487 and also A033833.

Factorizations are A001055, with image A045782.

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

Numbers whose number of factorizations is a power of 2 are A330977.

The least number with exactly prime(n) factorizations is A330992(n).

Cf. A002033, A045778, A045783, A318284, A330935, A330972, A330976, A330990, A330991, A331022.

Sequence in context: A014458 A099733 A350259 * A073902 A144207 A016487

Adjacent sequences: A330986 A330987 A330988 * A330990 A330991 A330992

Keyword

nonn,more

Author

Gus Wiseman, Jan 07 2020

Status

approved