OFFSET
1,2
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
EXAMPLE
The initial terms and a valid factorization of each are:
1 =
16 = 2*2*2*2
384 = 2*2*2*2*2*2*2*3
576 = 2*2*2*2*2*2*3*3
864 = 2*2*2*2*2*3*3*3
1296 = 2*2*2*2*3*3*3*3
1944 = 2*2*2*3*3*3*3*3
2916 = 2*2*3*3*3*3*3*3
4374 = 2*3*3*3*3*3*3*3
6561 = 3*3*3*3*3*3*3*3
131072 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*4
196608 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*3*4
262144 = 2*2*2*2*2*2*2*2*2*2*2*2*2*2*4*4
294912 = 2*2*2*2*2*2*2*2*2*2*2*2*2*3*3*4
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[1000], Select[facs[#], Length[#]==2^Max@@#&]!={}&]
CROSSREFS
Partitions of the prescribed type are counted by A340611.
The conjugate version is A340690.
A047993 counts balanced partitions.
A316439 counts factorizations by product and length.
A340596 counts co-balanced factorizations.
A340597 lists numbers with an alt-balanced factorization.
A340653 counts balanced factorizations.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 28 2021
EXTENSIONS
More terms from Chai Wah Wu, Feb 01 2021
STATUS
approved