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

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

Let p(n) = number of unitary divisors k of n, k

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)

Crossrefs

Cf. A116550, A225175, A225176.

Programs

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 *)

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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