OFFSET
1,4
EXAMPLE
The a(n) factorizations for n = 2, 4, 12, 24, 32, 48, 60, 96:
(4) (8) (24) (48) (64) (96) (120) (192)
(2*4) (4*6) (6*8) (2*32) (2*48) (2*60) (2*96)
(2*12) (2*24) (4*16) (4*24) (4*30) (4*48)
(4*12) (2*4*8) (6*16) (6*20) (6*32)
(2*4*6) (8*12) (10*12) (8*24)
(2*6*8) (2*6*10) (12*16)
(2*4*12) (4*6*8)
(2*4*24)
(2*6*16)
(2*8*12)
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[2*n], UnsameQ@@#&&OddQ[Times@@(#+1)]&]], {n, 100}]
CROSSREFS
The version for partitions instead of factorizations is A000009.
Positions of 1's are A004280.
The non-strict version is A340785.
Including odd n gives A357860.
A000005 counts divisors.
A001055 counts factorizations.
A001222 counts prime-power divisors.
A050361 counts strict factorizations into prime powers.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 17 2022
STATUS
approved