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A003271 Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.

%I A003271 M0531 #37 Oct 05 2017 17:21:48
%S A003271 1,2,3,4,5,9,16,17,41,83,113,137,257,773,977,1657,2048,2313,4001,5725,
%T A003271 7129,11117,17279,19897,22409,39283,43657,55457,120677,308941,314521,
%U A003271 465089,564353,797931,1110841,1310443,1924159,2535041,3637637,6001937,8319617,9453569,10969369
%N A003271 Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1.
%C A003271 A049865(a(n)) = n and A049865(m) <> n for m < a(n). [_Reinhard Zumkeller_, Aug 17 2011]
%D A003271 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003271 Donovan Johnson, <a href="/A003271/b003271.txt">Table of n, a(n) for n = 0..66</a> (terms < 10^10)
%H A003271 R. K. Guy, <a href="/A003271/a003271.pdf">Letter to N. J. A. Sloane, Apr 1975</a>
%H A003271 M. Lal, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0335419-3">Iterates of the unitary totient function</a>, Math. Comp., 28 (1974), 301-302.
%t A003271 uphi[n_ /; n <= 1] = 1; uphi[n_] := uphi[n] = (f = FactorInteger[n]; Times @@ (f[[All, 1]]^f[[All, 2]] - 1));
%t A003271 b[n_] := (k = 0; FixedPoint[(k++; uphi[#])&, n]; k - 1);
%t A003271 a[0] = 1; a[n_] := a[n] = For[an = a[n-1], True, an++, If[b[an] == n, Return[an]]];
%t A003271 Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 42}] (* _Jean-François Alcover_, Oct 05 2017 *)
%o A003271 (Haskell)
%o A003271 import Data.List (elemIndex)
%o A003271 import Data.Maybe (fromJust)
%o A003271 a003271 n = a003271_list !! n
%o A003271 a003271_list = map ((+ 1) . fromJust . (`elemIndex` a049865_list)) [0..]
%o A003271 -- _Reinhard Zumkeller_, Aug 17 2011
%Y A003271 Cf. A047994, A049865, A225172, A225173.
%K A003271 nonn,nice,easy
%O A003271 0,2
%A A003271 _N. J. A. Sloane_
%E A003271 More terms from _David W. Wilson_