A064559 Number of iterations in A064553 to reach a fixed point.

0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 3, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 3, 0, 2, 2, 1, 1, 0, 1, 1, 2, 0, 4, 1, 3, 1, 3, 2, 2, 1, 1, 2, 1, 0, 2, 1, 1, 3, 2, 0, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 3, 1, 2, 1, 2, 2, 3, 0, 2, 4, 1, 1, 2, 3, 3, 1, 0, 3, 1, 2, 1, 2, 2, 1, 2, 1, 3, 2, 1, 1, 1, 0, 4, 2, 1, 1, 1, 1, 3, 3, 2

Offset

1,7

Comments

This is well-defined since A064553(n) <= n.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(A003586(n)) = 0.

Example

a(12) = 0 as A064553(12) = 12.
a(26) = 3 as A064553(26) = 14, A064553(14) = 10, A064553(10) = 8 and A064553(8) = 8.

Mathematica

b[n_] := b[n] = If[n == 1, 1, Times @@ (PrimePi[#[[1]]]^#[[2]]& /@ FactorInteger[n])];
c[n_] := c[n] = If[n == 1, 1, If[PrimeQ[n], Prime[PrimePi[n] + 1], Times @@ (c[#1]^#2& @@@ FactorInteger[n])]];
A064553[n_] := b[c[n]];
a[n_] := Length[FixedPointList[A064553, n]] - 2;
Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *)

Prog

(Scheme) (define (A064559 n) (let ((k (A064553 n))) (if (= k n) 0 (+ 1 (A064559 k))))) ;; Antti Karttunen, Jul 23 2017

Crossrefs

Cf. A064553.

Sequence in context: A326016 A326033 A029429 * A380385 A340998 A336562

Adjacent sequences: A064556 A064557 A064558 * A064560 A064561 A064562

Keyword

nonn

Author

Reinhard Zumkeller, Sep 21 2001

Status

approved