cp's OEIS Frontend

A346213 Number of iterations of A000688 needed to reach 1 starting at n (n is counted).

%I A346213 #13 Oct 15 2023 05:12:24
%S A346213 1,2,2,3,2,2,2,3,3,2,2,3,2,2,2,3,2,3,2,3,2,2,2,3,3,2,3,3,2,2,2,3,2,2,
%T A346213 2,4,2,2,2,3,2,2,2,3,3,2,2,3,3,3,2,3,2,3,2,3,2,2,2,3,2,2,3,3,2,2,2,3,
%U A346213 2,2,2,3,2,2,3,3,2,2,2,3,3,2,2,3,2,2,2
%N A346213 Number of iterations of A000688 needed to reach 1 starting at n (n is counted).
%C A346213 The least value of n such that a(n) = 1, 2, ..., 5 is 1, 2, 4, 36 and 264600.
%H A346213 Amiram Eldar, <a href="/A346213/b346213.txt">Table of n, a(n) for n = 1..10000</a>
%H A346213 Paul Erdős and Aleksandar Ivić, <a href="https://www.jstor.org/stable/44095772">On the iterates of the enumerating function of finite abelian groups</a>, Bulletin Académie serbe des sciences et des arts, Classe des sciences mathématiques et naturelles, Sciences mathématiques, No. 17 (1989), pp. 13-22; <a href="https://www.renyi.hu/~p_erdos/1989-23.pdf">alternative link</a>.
%F A346213 Sum_{k<=x} a(k) ~ c*x + O(x^(1/2 + eps)), where c > 1 is a constant (Erdős and Ivić, 1989).
%e A346213 a(4) = 3 since the trajectory of n = 4, {n, A000688(n), A000688(A000688(n))} = {4, 2, 1}, has the length 3.
%t A346213 a[n_] := -1 + Length @ FixedPointList[FiniteAbelianGroupCount, n]; Array[a, 100]
%Y A346213 Cf. A000688, A060937.
%K A346213 nonn
%O A346213 1,2
%A A346213 _Amiram Eldar_, Jul 10 2021