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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

Table of n, a(n) for n=1..87.

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.)