Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
proposed
approved
editing
proposed
Least number positive integer with exactly 2^n factorizations into factors > 1, and or 0 if none no such integer exists.
allocated for Gus WisemanLeast number with exactly 2^n factorizations into factors > 1, and 0 if none exists.
1, 4, 12, 0, 72, 0, 480
0,2
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)
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.
allocated
nonn,more
Gus Wiseman, Jan 07 2020
approved
editing
allocating
allocated
allocated for Gus Wiseman
allocating
approved