

A003271


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


12



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
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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), 301302.


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[n1], True, an++, If[b[an] == n, Return[an]]];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 42}] (* JeanFrançois 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



