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A368899
Least integer which begins n consecutive integers with the same prime tower factorization tree.
1
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
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 â„•atural 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
Sequence in context: A132567 A269632 A083459 * A034173 A132519 A117969
KEYWORD
nonn,more
AUTHOR
Roberto Conti, Jan 09 2024
STATUS
approved