A225172 Largest number which requires n iterations of the unitary totient function (A047994) to reach 1.

1, 2, 6, 14, 42, 86, 186, 462, 930, 1986, 4170, 6510, 14682, 29366, 50342, 73410, 189498, 287654, 491190, 849570, 1699142, 2433878, 4280774, 7978218, 14442690, 25900142, 44400390, 78492954, 123958794, 228018066, 355388970, 629582370, 780686294

Offset: 0

Author

N. J. A. Sloane, May 01 2013

Keywords

• nonn

Comments

Searched up to 10^10. a(33) >= 1609056138. a(34) >= 2275537110. a(35) >= 4171607222. - Donovan Johnson, May 02 2013

Links

• M. Lal, Iterates of the unitary totient function, Math. Comp., 28 (1974), 301-302.

Crossrefs

Cf. A047994, A003271, A225173.

Programs

Mathematica

(* This is just a verification of recorded data up to a(23), assuming a(n-1)/2 <= a(n) <= 4*a(n-1) *) uphi[n_] := (cnt++; fi = FactorInteger[n]; Times @@ (fi[[All, 1]]^fi[[All, 2]] - 1)); f[n_] := (cnt = 0; NestWhile[uphi, n, # > 1 &]; cnt); a[0] = 1; a[1] = 2; a[n_] := a[n] = (For[record = k = a[n-1]/2//Floor, k <= 4*a[n-1], k++, If[f[k] == n, record = k]]; record); Table[Print[a[n]]; a[n], {n, 0, 23}] (* Jean-François Alcover, May 02 2013 *)

Formula

a(n) = max{x : A049865(x) = n}. - R. J. Mathar, May 02 2013

Extensions

a(16)-a(32) from Donovan Johnson, May 02 2013