OFFSET
1,12
COMMENTS
EXAMPLE
The a(n) ordered factorizations with at least one pair of adjacent equal factors for n = 12, 24, 36, 60:
2*2*3 2*2*6 6*6 15*2*2
3*2*2 6*2*2 2*2*9 2*2*15
2*2*2*3 3*3*4 2*2*3*5
2*2*3*2 4*3*3 2*2*5*3
2*3*2*2 9*2*2 3*2*2*5
3*2*2*2 2*2*3*3 3*5*2*2
2*3*3*2 5*2*2*3
3*2*2*3 5*3*2*2
3*3*2*2
See also examples in A348611.
MATHEMATICA
ordfacs[n_]:=If[n<=1, {{}}, Join@@Table[Prepend[#, d]&/@ordfacs[n/d], {d, Rest[Divisors[n]]}]];
antirunQ[y_]:=Length[y]==Length[Split[y]]
Table[Length[Select[ordfacs[n], !antirunQ[#]&]], {n, 100}]
CROSSREFS
Positions of 0's are A005117.
Positions of 4's appear to be A030514.
Positions of 2's appear to be A054753.
Positions of 1's appear to be A168363.
Factorizations with a permutation of this type are counted by A333487.
Factorizations without a permutation of this type are counted by A335434.
The complement is counted by A348611.
Dominated by A348613 (non-alternating ordered factorizations).
A339846 counts even-length factorizations.
A339890 counts odd-length factorizations.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 08 2021
STATUS
approved