OFFSET
1,9
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
EXAMPLE
The a(n) factorizations for n = 45, 108, 135, 180, 252:
(45) (4*27) (135) (4*45) (4*63)
(5*9) (2*6*9) (3*45) (12*15) (12*21)
(3*15) (3*4*9) (5*27) (4*5*9) (4*7*9)
(3*3*5) (2*2*27) (9*15) (2*2*45) (6*6*7)
(2*2*3*9) (3*5*9) (2*6*15) (2*2*63)
(2*2*3*3*3) (3*3*15) (3*4*15) (2*6*21)
(3*3*3*5) (2*2*5*9) (3*4*21)
(3*3*4*5) (2*2*7*9)
(2*2*3*15) (2*3*6*7)
(2*2*3*3*5) (3*3*4*7)
(2*2*3*21)
(2*2*3*3*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@*Max]], {n, 100}]
PROG
(PARI) A340831(n, m=n, fc=1) = if(1==n, !fc, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&(!fc||(d%2)), s += A340831(n/d, d, 0*fc))); (s)); \\ Antti Karttunen, Dec 13 2021
CROSSREFS
Positions of 0's are A000079.
The version for partitions is A027193.
The version for prime indices is A244991.
The version looking at length instead of greatest factor is A339890.
The version that also has odd length is A340607.
The version looking at least factor is A340832.
- Factorizations -
A001055 counts factorizations.
A045778 counts strict factorizations.
A316439 counts factorizations by product and length.
A340653 counts balanced factorizations.
- Odd -
A000009 counts partitions into odd parts.
A024429 counts set partitions of odd length.
A026424 lists numbers with odd Omega.
A058695 counts partitions of odd numbers.
A066208 lists numbers with odd-indexed prime factors.
A174726 counts ordered factorizations of odd length.
A340692 counts partitions of odd rank.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 04 2021
EXTENSIONS
Data section extended up to 108 terms by Antti Karttunen, Dec 13 2021
STATUS
approved