OFFSET
1,12
COMMENTS
An ordered factorization of n is a finite sequence of positive integers > 1 with product n.
A sequence is alternating if it is alternately strictly increasing and strictly decreasing, starting with either.
LINKS
EXAMPLE
The a(n) ordered factorizations for n = 4, 12, 16, 24, 32, 36:
2*2 2*2*3 4*4 2*2*6 2*2*8 6*6
3*2*2 2*2*4 2*3*4 2*4*4 2*2*9
4*2*2 4*3*2 4*4*2 2*3*6
2*2*2*2 6*2*2 8*2*2 3*3*4
2*2*2*3 2*2*2*4 4*3*3
2*2*3*2 2*2*4*2 6*3*2
2*3*2*2 2*4*2*2 9*2*2
3*2*2*2 4*2*2*2 2*2*3*3
2*2*2*2*2 2*3*3*2
3*2*2*3
3*3*2*2
MATHEMATICA
ordfacs[n_]:=If[n<=1, {{}}, Join@@Table[Prepend[#, d]&/@ordfacs[n/d], {d, Rest[Divisors[n]]}]];
wigQ[y_]:=Or[Length[y]==0, Length[Split[y]]==Length[y]&&Length[Split[Sign[Differences[y]]]]==Length[y]-1];
Table[Length[Select[ordfacs[n], !wigQ[#]&]], {n, 100}]
CROSSREFS
The complement is counted by A348610.
A001250 counts alternating permutations.
A339846 counts even-length factorizations.
A339890 counts odd-length factorizations.
A348611 counts anti-run ordered factorizations.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 03 2021
STATUS
approved