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A330989 Least positive integer with exactly 2^n factorizations into factors > 1, or 0 if no such integer exists. 11
1, 4, 12, 0, 72, 0, 480 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 09:12 EST 2022. Contains 350454 sequences. (Running on oeis4.)