login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A340596 Number of co-balanced factorizations of n. 25
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,12
COMMENTS
We define a factorization of n into factors > 1 to be co-balanced if it has exactly A001221(n) factors.
LINKS
EXAMPLE
The a(n) co-balanced factorizations for n = 12, 24, 36, 72, 120, 144, 180:
2*6 3*8 4*9 8*9 3*5*8 2*72 4*5*9
3*4 4*6 6*6 2*36 4*5*6 3*48 5*6*6
2*12 2*18 3*24 2*2*30 4*36 2*2*45
3*12 4*18 2*3*20 6*24 2*3*30
6*12 2*4*15 8*18 2*5*18
2*5*12 9*16 2*6*15
2*6*10 12*12 2*9*10
3*4*10 3*3*20
3*4*15
3*5*12
3*6*10
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], Length[#]==PrimeNu[n]&]], {n, 100}]
CROSSREFS
Positions of terms > 1 are A126706.
Positions of 1's are A303554.
The version for unlabeled multiset partitions is A319616.
The alt-balanced version is A340599.
The balanced version is A340653.
The cross-balanced version is A340654.
The twice-balanced version is A340655.
A001055 counts factorizations.
A045778 counts strict factorizations.
A316439 counts factorizations by product and length.
Other balance-related sequences:
- A010054 counts balanced strict partitions.
- A047993 counts balanced partitions.
- A098124 counts balanced compositions.
- A106529 lists Heinz numbers of balanced partitions.
- A340597 lists numbers with an alt-balanced factorization.
- A340598 counts balanced set partitions.
- A340600 counts unlabeled balanced multiset partitions.
Sequence in context: A030612 A327528 A264857 * A340654 A303837 A286520
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 15 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 06:21 EST 2024. Contains 370240 sequences. (Running on oeis4.)