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

0,2

Comments

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

Links

Table of n, a(n) for n=0..32.

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

Formula

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

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 *)

Crossrefs

Cf. A047994, A003271, A225173.

Sequence in context: A004066 A123383 A281707 * A212197 A151414 A151386

Adjacent sequences: A225169 A225170 A225171 * A225173 A225174 A225175

Keyword

nonn

Author

N. J. A. Sloane, May 01 2013

Extensions

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

Status

approved