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URL: https://oeis.org/A003271

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A003271
Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.
17
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
0,2
COMMENTS
A049865(a(n)) = n and A049865(m) <> n for m < a(n). [Reinhard Zumkeller, Aug 17 2011]
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)
M. Lal, Iterates of the unitary totient function, Math. Comp., 28 (1974), 301-302.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,nice,easy
EXTENSIONS
More terms from David W. Wilson
STATUS
approved