|
|
A331200
|
|
Least number with each record number of factorizations into distinct factors > 1.
|
|
7
|
|
|
1, 6, 12, 24, 48, 60, 96, 120, 180, 240, 360, 480, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 4320, 5040, 7560, 8640, 10080, 15120, 20160, 25200, 30240, 40320, 45360, 50400, 55440, 60480, 75600, 90720, 100800, 110880, 120960, 151200, 181440, 221760
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
First differs from A330997 in lacking 64.
|
|
LINKS
|
|
|
EXAMPLE
|
Strict factorizations of the initial terms:
() (6) (12) (24) (48) (60) (96) (120)
(2*3) (2*6) (3*8) (6*8) (2*30) (2*48) (2*60)
(3*4) (4*6) (2*24) (3*20) (3*32) (3*40)
(2*12) (3*16) (4*15) (4*24) (4*30)
(2*3*4) (4*12) (5*12) (6*16) (5*24)
(2*3*8) (6*10) (8*12) (6*20)
(2*4*6) (2*5*6) (2*6*8) (8*15)
(3*4*5) (3*4*8) (10*12)
(2*3*10) (2*3*16) (3*5*8)
(2*4*12) (4*5*6)
(2*3*20)
(2*4*15)
(2*5*12)
(2*6*10)
(3*4*10)
(2*3*4*5)
|
|
MATHEMATICA
|
nn=1000;
strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
qv=Table[Length[strfacs[n]], {n, nn}];
Table[Position[qv, i][[1, 1]], {i, Union[qv//.{foe___, x_, y_, afe___}/; x>y:>{foe, x, afe}]}]
|
|
CROSSREFS
|
This is the strict version of highly factorable numbers A033833.
The least number with n strict factorizations is A330974(n).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|