Number
Value
42
Matula number
42
Tree Properties
Nodes
—
Depth
—
Leaves
—
Branching factor
—
Is prime
—
Tree type
—
Arithmetic Functions
μ(n) Möbius
—
λ(n) Liouville
—
Ω(n) prime factors
—
ω(n) distinct primes
—
How it works: In Matula’s bijection, 1 maps to a single node.
A prime pk (the k-th prime) maps to a root connected to the tree for k.
A composite n = a × b × c… maps to a root whose children are the trees for a, b, c…
Every natural number produces a unique tree. Every rooted tree has a unique number.