OFFSET
1,8
COMMENTS
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The a(n) factorizations for n = 120, 960, 5760, 6720:
120 960 5760 6720
4*5*6 2*16*30 16*18*20 4*30*56
2*6*10 4*12*20 3*5*6*8*8 10*21*32
8*10*12 4*4*6*6*10 12*20*28
3*4*4*4*5 2*2*8*10*18 4*5*6*7*8
2*2*2*4*4*5*9 2*4*7*10*12
2*2*2*4*5*6*7
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], OddQ[Length[#]]&&Mean[#]==Median[#]&]], {n, 100}]
CROSSREFS
A001055 counts factorizations.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 24 2023
STATUS
approved