A368899 - OEIS

%I #22 Jan 14 2024 09:02:19

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

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

%C 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].

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

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

%H Roberto Conti, Pierluigi Contucci, and Vitalii Iudelevich, <a href="https://arxiv.org/abs/2401.03278">Bounds on tree distribution in number theory</a>, arXiv:2401.03278 [math.NT], 2023. See Section 5 (p. 13).

%H Roberto Conti and Pierluigi Contucci, <a href="https://arxiv.org/abs/2204.08982">A ℕatural Avenue</a>, arXiv:2204.08982 [math.NT], 2023.

%e For n=5, a(5) = 136824 = 2^3 * 3^1 * 5701^1 has tree structure

%e    136824

%e    / | \

%e   3  1  1

%e   |

%e   1

%e The structures of the 5 numbers 136824, ..., 136828 are isomorphic as rooted trees, for example

%e    136826

%e    / | \

%e   1  2  1

%e      |

%e      1

%Y Cf. A034173, A369015.

%K nonn,more

%O 1,2

%A _Roberto Conti_, Jan 09 2024