A034173 -id:A034173 - cp's OEIS frontend

A218865 First of a run of 7 consecutive numbers with same prime signature.

440738966073, 464881210073, 645462662449, 914549532721, 932537185321, 936083045673, 1043710445721, 1091100709673, 1225660528209, 1349165568945, 1602377996921, 1682159750473, 1714275593649, 1730241245545, 1756186304521, 1872671302049, 1956516794721, 1987087485225

Offset: 1

Donovan Johnson, Nov 08 2012

nonn

a(1) = A034173(7) = A218455(443) = A218455(444)-1.

a(19) > 2*10^12. - Donovan Johnson, May 11 2013

			The 7 consecutive numbers from 645462662449 to 645462662455 all have a prime signature of 2,1,1,1.

Cf. A034173, A034174, A052213, A052214, A175590, A218448, A218455.

a(7)-a(18) from Donovan Johnson, May 11 2013

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

Original entry on oeis.org

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

Offset: 1

Roberto Conti, Jan 09 2024

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.

			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

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.

Cf. A034173, A369015.

cp's OEIS Frontend

A218865 First of a run of 7 consecutive numbers with same prime signature.

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