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 A346213 Number of iterations of A000688 needed to reach 1 starting at n (n is counted). 0
 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, 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, 2, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The least value of n such that a(n) = 1, 2, ..., 5 is 1, 2, 4, 36 and 264600. LINKS Paul Erdős and Aleksandar Ivić, On the iterates of the enumerating function of finite abelian groups, Bulletin Académie serbe des sciences et des arts, Classe des sciences mathématiques et naturelles, Sciences mathématiques, No. 17 (1989), pp. 13-22; alternative link. FORMULA Sum_{k<=x} a(k) ~ c*x + O(x^(1/2 + eps)), where c > 1 is a constant (Erdős and Ivić, 1989). EXAMPLE a(4) = 3 since the trajectory of n = 4, {n, A000688(n), A000688(A000688(n))} = {4, 2, 1}, has the length 3. MATHEMATICA a[n_] := -1 + Length @ FixedPointList[FiniteAbelianGroupCount, n]; Array[a, 100] CROSSREFS Cf. A000688, A060937. Sequence in context: A104517 A098397 A278744 * A082091 A334216 A100549 Adjacent sequences:  A346210 A346211 A346212 * A346214 A346215 A346217 KEYWORD nonn AUTHOR Amiram Eldar, Jul 10 2021 STATUS approved

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Last modified September 17 17:29 EDT 2021. Contains 347489 sequences. (Running on oeis4.)