A319138 Number of complete strict planar branching factorizations of n.

0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 4, 1, 2, 2, 0, 1, 4, 1, 4, 2, 2, 1, 8, 0, 2, 0, 4, 1, 18, 1, 0, 2, 2, 2, 28, 1, 2, 2, 8, 1, 18, 1, 4, 4, 2, 1, 16, 0, 4, 2, 4, 1, 8, 2, 8, 2, 2, 1, 84, 1, 2, 4, 0, 2, 18, 1, 4, 2, 18, 1, 112, 1, 2, 4, 4, 2, 18, 1, 16, 0, 2, 1

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. A strict planar branching factorization is complete if the leaves are all prime numbers.

Links

Table of n, a(n) for n=1..83.

Formula

a(prime^n) = A000007(n - 1).

a(product of n distinct primes) = A032037(n).

Example

The a(12) = 4 trees: (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[Select[sotfs[n], FreeQ[#, _Integer?(!PrimeQ[#]&)]&]], {n, 100}]

Crossrefs

Cf. A000108, A045778, A074206, A118376, A277130, A281113, A281118, A295279, A295281, A317144, A319122, A319123, A319136, A319137.

Sequence in context: A136176 A291914 A303708 * A349396 A330462 A281081

Adjacent sequences: A319135 A319136 A319137 * A319139 A319140 A319141

Keyword

nonn

Author

Gus Wiseman, Sep 11 2018

Status

approved