A368899 Least integer which begins n consecutive integers with the same prime tower factorization tree.

1, 2, 33, 19940, 136824, 630772, 30530822

Offset

1,2

Comments

The (unordered) prime tower tree for k having prime factorization k = Product p[i]^e[i] comprises a root vertex and beneath it child subtrees with tree numbers e[i].

a(n) is the smallest k such that A369015(k) = A369015(k+i) for 1 <= i < n.

a(n) <= A034173(n) since it demands equal exponents but here they only have to be isomorphic.

Links

Table of n, a(n) for n=1..7.

Roberto Conti, Pierluigi Contucci, and Vitalii Iudelevich, Bounds on tree distribution in number theory, arXiv:2401.03278 [math.NT], 2023. See Section 5 (p. 13).

Roberto Conti and Pierluigi Contucci, A ℕatural Avenue, arXiv:2204.08982 [math.NT], 2023.

Example

For n=5, a(5) = 136824 = 2^3 * 3^1 * 5701^1 has tree structure
   136824
   / | \
  3  1  1
  |
  1
The structures of the 5 numbers 136824, ..., 136828 are isomorphic as rooted trees, for example
   136826
   / | \
  1  2  1
     |
     1

Crossrefs

Cf. A034173, A369015.

Sequence in context: A132567 A269632 A083459 * A034173 A132519 A117969

Adjacent sequences: A368896 A368897 A368898 * A368900 A368901 A368902

Keyword

nonn,more

Author

Roberto Conti, Jan 09 2024

Status

approved