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A330972
Sorted list containing the least number with each possible nonzero number of factorizations into factors > 1.
38
1, 4, 8, 12, 16, 24, 36, 48, 60, 72, 96, 120, 128, 144, 180, 192, 216, 240, 256, 288, 360, 384, 420, 432, 480, 576, 720, 768, 840, 864, 900, 960, 1024, 1080, 1152, 1260, 1440, 1680, 1728, 1800, 1920, 2048, 2160, 2304, 2520, 2592, 2880, 3072, 3360, 3456, 3600
OFFSET
1,2
COMMENTS
This is the sorted list of positions of first appearances in A001055 of each element of the range (A045782).
LINKS
R. E. Canfield, P. Erdős and C. Pomerance, On a Problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory 17 (1983), 1-28.
EXAMPLE
Factorizations of n for n = 4, 8, 12, 16, 24, 36, 48, 60:
4 8 12 16 24 36 48 60
2*2 2*4 2*6 2*8 3*8 4*9 6*8 2*30
2*2*2 3*4 4*4 4*6 6*6 2*24 3*20
2*2*3 2*2*4 2*12 2*18 3*16 4*15
2*2*2*2 2*2*6 3*12 4*12 5*12
2*3*4 2*2*9 2*3*8 6*10
2*2*2*3 2*3*6 2*4*6 2*5*6
3*3*4 3*4*4 3*4*5
2*2*3*3 2*2*12 2*2*15
2*2*2*6 2*3*10
2*2*3*4 2*2*3*5
2*2*2*2*3
MATHEMATICA
nn=1000;
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
nds=Length/@Array[facs, nn];
Table[Position[nds, i][[1, 1]], {i, First/@Gather[nds]}]
CROSSREFS
All terms belong to A025487
Includes all highly factorable numbers A033833.
Factorizations are A001055, with image A045782.
The least number with A045782(n) factorizations is A045783(n).
The least number with n factorizations is A330973(n).
The strict version is A330997.
Sequence in context: A329883 A066192 A097981 * A033833 A291834 A291928
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 06 2020
STATUS
approved