A003271 Smallest number that requires n iterations of the unitary totient function (A047994) to reach 1. (Formerly M0531)

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)

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.

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

Cf. A047994, A049865, A225172, A225173.

Sequence in context: A068584 A107799 A329049 * A049796 A106165 A305237

Adjacent sequences: A003268 A003269 A003270 * A003272 A003273 A003274

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from David W. Wilson

Status

approved