OFFSET
1,4
COMMENTS
An ordered factorization of n is a finite sequence of positive integers > 1 with product n.
We define a sequence to be weakly alternating if it is alternately weakly increasing and weakly decreasing, starting with either.
FORMULA
a(2^n) = A349052(n).
EXAMPLE
The ordered factorizations for n = 2, 4, 6, 8, 12, 24, 30:
(2) (4) (6) (8) (12) (24) (30)
(2*2) (2*3) (2*4) (2*6) (3*8) (5*6)
(3*2) (4*2) (3*4) (4*6) (6*5)
(2*2*2) (4*3) (6*4) (10*3)
(6*2) (8*3) (15*2)
(2*2*3) (12*2) (2*15)
(2*3*2) (2*12) (3*10)
(3*2*2) (2*2*6) (2*5*3)
(2*4*3) (3*2*5)
(2*6*2) (3*5*2)
(3*2*4) (5*2*3)
(3*4*2)
(4*2*3)
(6*2*2)
(2*2*2*3)
(2*2*3*2)
(2*3*2*2)
(3*2*2*2)
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
whkQ[y_]:=And@@Table[If[EvenQ[m], y[[m]]<=y[[m+1]], y[[m]]>=y[[m+1]]], {m, 1, Length[y]-1}];
Table[Length[Select[Join@@Permutations/@facs[n], whkQ[#]||whkQ[-#]&]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 04 2021
STATUS
approved