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A005424 Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
(Formerly M0530)
5
2, 3, 4, 5, 8, 9, 13, 16, 17, 24, 25, 35, 44, 63, 64, 91, 97, 128, 193, 221, 259, 324, 353, 391, 477, 702, 929, 1188, 1269, 1589, 1613, 2017, 2309, 2623, 3397, 4064, 4781, 5468, 6515, 6887, 9213, 12286, 12887, 14009, 16564, 16897, 17803, 30428, 36256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Let p(n) = number of unitary divisors k of n, k<n, that are relatively prime to n. Let p_1(n) = p(n), p_r(n) = p(p_{r-1}(n)). Sequence gives minimal r such that p_r(n)=1.

REFERENCES

M. Lal, H. Wareham and R. Mifflin, Iterates of the bi-unitary totient function, Utilitas Math., 10 (1976), 347-350.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..78 (terms < 5*10^6)

MAPLE

L := [seq(0, i=0..100)] ;

for n from 1 do

    itr := A225320(n) ;

    if itr < nops(L) then

        if op(itr, L) = 0 then

            L := subsop(itr=n, L) ;

            print(L) ;

        end if;

    end if;

end do: # R. J. Mathar, May 02 2013

MATHEMATICA

A116550[1] = 1; A116550[n_] := With[{pp = Power @@@ FactorInteger[n]}, Count[Range[n], m_ /; Intersection[pp, Power @@@ FactorInteger[m]] == {}]]; A225320[n_] := A225320[n] = If[n == 1, 0, 1+A225320[A116550[n]]]; L = Array[0&, 100]; For[n = 1, n <= 40000, n++, itr = A225320[n]; If[itr < Length[L], If[L[[itr]] == 0, L = ReplacePart[L, itr -> n]; Print[Select[L, Positive] // Last]]]]; Select[L, Positive] (* Jean-Fran├žois Alcover, Jan 13 2014, after R. J. Mathar *)

CROSSREFS

Cf. A116550, A225175, A225176.

Sequence in context: A165652 A191851 A063678 * A105317 A342094 A094103

Adjacent sequences:  A005421 A005422 A005423 * A005425 A005426 A005427

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 28 19:33 EDT 2021. Contains 346335 sequences. (Running on oeis4.)