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

Author

Reinhard Zumkeller, Sep 21 2001

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A064553.

Programs

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 *)

Scheme

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

Formula

a(A003586(n)) = 0.