A319137 Number of strict planar branching factorizations of n.

1, 1, 1, 1, 1, 3, 1, 3, 1, 3, 1, 9, 1, 3, 3, 7, 1, 9, 1, 9, 3, 3, 1, 37, 1, 3, 3, 9, 1, 25, 1, 21, 3, 3, 3, 57, 1, 3, 3, 37, 1, 25, 1, 9, 9, 3, 1, 161, 1, 9, 3, 9, 1, 37, 3, 37, 3, 3, 1, 153, 1, 3, 9, 75, 3, 25, 1, 9, 3, 25, 1, 345, 1, 3, 9, 9, 3, 25, 1, 161

Offset

1,6

Comments

A strict planar branching factorization of n is either the number n itself or a sequence of at least two strict planar branching factorizations, one of each factor in a strict ordered factorization of n.

Links

Table of n, a(n) for n=1..80.

Formula

a(prime^n) = A319123(n + 1).

a(product of n distinct primes) = A319122(n).

Example

The a(12) = 9 trees:
  12,
  (2*6), (3*4), (4*3),(6*2),
  (2*(2*3)), (2*(3*2)), ((2*3)*2), ((3*2)*2).

Mathematica

ordfacs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@ordfacs[n/d], {d, Rest[Divisors[n]]}]]
sotfs[n_]:=Prepend[Join@@Table[Tuples[sotfs/@f], {f, Select[ordfacs[n], And[Length[#]>1, UnsameQ@@#]&]}], n];
Table[Length[sotfs[n]], {n, 100}]

Crossrefs

Cf. A000108, A001055, A045778, A074206, A118376, A277130, A281113, A281118, A292504, A295279, A295281, A317144, A319122, A319123, A319138.

Sequence in context: A348611 A070039 A227991 * A074122 A335182 A319992

Adjacent sequences: A319134 A319135 A319136 * A319138 A319139 A319140

Keyword

nonn

Author

Gus Wiseman, Sep 11 2018

Status

approved