A003271 Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.
1, 2, 3, 4, 5, 9, 16, 17, 41, 83, 113, 137, 257, 773, 977, 1657, 2048, 2313, 4001, 5725, 7129, 11117, 17279, 19897, 22409, 39283, 43657, 55457, 120677, 308941, 314521, 465089, 564353, 797931, 1110841, 1310443, 1924159, 2535041, 3637637, 6001937, 8319617, 9453569, 10969369
Offset: 0
References
- 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 = 0..66 (terms < 10^10)
- R. K. Guy, Letter to N. J. A. Sloane, Apr 1975
- M. Lal, Iterates of the unitary totient function, Math. Comp., 28 (1974), 301-302.
Programs
-
Haskell
import Data.List (elemIndex) import Data.Maybe (fromJust) a003271 n = a003271_list !! n a003271_list = map ((+ 1) . fromJust . (`elemIndex` a049865_list)) [0..] -- Reinhard Zumkeller, Aug 17 2011
-
Mathematica
uphi[n_ /; n <= 1] = 1; uphi[n_] := uphi[n] = (f = FactorInteger[n]; Times @@ (f[[All, 1]]^f[[All, 2]] - 1)); b[n_] := (k = 0; FixedPoint[(k++; uphi[#])&, n]; k - 1); a[0] = 1; a[n_] := a[n] = For[an = a[n-1], True, an++, If[b[an] == n, Return[an]]]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 42}] (* Jean-François Alcover, Oct 05 2017 *)
Extensions
More terms from David W. Wilson
Comments