A005424 Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1. (Formerly M0530)

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

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

Amiram Eldar, Table of n, a(n) for n = 1..97 (terms 1..78 from Donovan Johnson)

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-François 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