OFFSET
1,64
COMMENTS
Also factorizations whose number of factors is divisible by their least common multiple.
EXAMPLE
The a(n) factorizations for n = 8192, 46656, 73728:
2*2*2*2*2*4*8*8 6*6*6*6*6*6 2*2*2*2*2*2*2*2*2*4*6*6
2*2*2*2*4*4*4*8 2*2*2*2*2*2*3*3*3*3*3*3 2*2*2*2*2*2*2*2*3*4*4*6
2*2*2*4*4*4*4*4 2*2*2*2*2*2*2*3*3*4*4*4
2*2*2*2*2*2*2*2*2*2*2*4 2*2*2*2*2*2*2*2*2*2*6*12
2*2*2*2*2*2*2*2*2*3*4*12
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], And@@IntegerQ/@(Length[#]/#)&]], {n, 100}]
CROSSREFS
Positions of nonzero terms are A340852.
The reciprocal version is A340853.
A320911 can be factored into squarefree semiprimes.
A340597 have an alt-balanced factorization.
- Factorizations -
A316439 counts factorizations by product and length.
A339846 counts factorizations of even length.
A339890 counts factorizations of odd length.
A340653 counts balanced factorizations.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 04 2021
STATUS
approved