OFFSET
1,3
COMMENTS
A terminal subtree is a vertex and all its descendents.
Row n has length A317713(n).
Row n begins with 1 which is a singleton (single childless vertex), and ends with n itself which is the whole tree.
The second-last term in row n >= 1 is the largest (by tree number) child subtree of the root, which is A061395(n).
A factor of 2 in a tree number is a singleton child, and tree number 2^c is a vertex with c singleton children and no other children.
The second term in each row is T(n,2) = 2^c for the subtree with the fewest singleton children and no other children.
A rooted star is n = 2^c and these are the only rows of length 2.
LINKS
FORMULA
row(n) = union of row(primepi(p)) for each p a prime factor of n, followed by n itself.
EXAMPLE
Triangle begins:
k=1 2 3 4
n=1: 1,
n=2: 1, 2,
n=3: 1, 2, 3,
n=4: 1, 4,
n=5: 1, 2, 3, 5,
n=6: 1, 2, 6,
n=7: 1, 4, 7,
For n=78, tree 78 and its subtree numbers are
78
/ | \
1 2 6 distinct tree numbers
| | \ row(78) = {1, 2, 6, 78}
1 1 2
|
1
PROG
(PARI) \\ See links.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Kevin Ryde, Jun 08 2022
STATUS
approved