

A225320


The number of iterations of the biunitary totient A116550 needed to reach 1 starting with n.


2



0, 1, 2, 3, 4, 3, 4, 5, 6, 4, 5, 6, 7, 7, 7, 8, 9, 7, 8, 8, 8, 8, 9, 10, 11, 8, 9, 9, 10, 8, 9, 10, 10, 11, 12, 11, 12, 10, 10, 10, 11, 9, 10, 13, 12, 11, 12, 12, 13, 12, 13, 10, 11, 11, 10, 12, 10, 10, 11, 12, 13, 13, 14, 15, 13, 13, 14, 13, 14, 11, 12, 14, 15, 12, 13, 15, 14, 10, 11, 14
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OFFSET

1,3


LINKS

Table of n, a(n) for n=1..80.


FORMULA

The smallest x such that A116550^x(n)=1, where the operation Op^x denotes x nestings of the operator Op.


EXAMPLE

a(6)=3 because the first step is A116550(6) = 3, the second A116550(3)=2, the third A116550(2)=1, where 1 is reached.


MAPLE

A225320 := proc(n)
option remember;
if n = 1 then
0;
else
1+procname(A116550(n)) ;
end if;
end proc:


MATHEMATICA

A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; a[n_] := a[n] = If[n == 1, 0, 1 + a[A116550[n]]]; Table[a[n], {n, 1, 80}] (* JeanFrançois Alcover, Dec 16 2013 *)


CROSSREFS

Cf. A005424 (positions of records)
Sequence in context: A307531 A125619 A262519 * A308937 A123066 A330239
Adjacent sequences: A225317 A225318 A225319 * A225321 A225322 A225323


KEYWORD

nonn


AUTHOR

R. J. Mathar, May 05 2013


STATUS

approved



