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A340765
Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 6, 2, 1.
2
6, 7, 9, 14, 18, 19, 27, 38, 54, 81, 162, 163, 243, 326, 486, 487, 729, 974, 1458, 1459, 2187, 2918, 4374, 6561, 13122, 19683, 39366, 39367, 59049, 78734, 118098, 177147, 354294, 531441, 1062882, 1594323, 3188646, 4782969, 9565938, 14348907, 28697814, 43046721, 86093442, 86093443, 129140163, 172186886
OFFSET
1,1
COMMENTS
Infinite set (see reference).
Contains 3^k for k >= 2 and 2*3^k for k >= 1, and all members of A111974 except 3. - Robert Israel, Dec 23 2021
LINKS
Eliot T. Jacobson and Alan E. Parks, Infinite branches of the phi-tree, Amer. Math. Monthly, Vol. 93, No. 7 (August-September 1986), pp. 552-554.
EXAMPLE
19 is in the list because phi(phi(19)) = phi(18) = 6.
MAPLE
R:= {6}: Agenda:= {6}: count:= 1:
while count - nops(Agenda) < 99 do
v:= min(Agenda);
W:= convert(numtheory:-invphi(v), set);
count:= count + nops(W);
Agenda:= Agenda minus {v} union W;
R:= R union W;
od:
sort(select(`<=`, convert(R, list), min(Agenda))); # Robert Israel, Dec 23 2021
MATHEMATICA
Select[Range[4, 10000], FixedPointList[EulerPhi, #][[-4]] == 6 &] (* Amiram Eldar, Jan 27 2021 *)
PROG
(PARI) isok(k) = if (k>=6, while((k!=6) && (k!=4), k=eulerphi(k))); k == 6; \\ Michel Marcus, Feb 01 2021
CROSSREFS
Cf. A000010, A340762 (complement relative to {n>=4}).
Sequence in context: A168614 A045014 A047591 * A239869 A289547 A329912
KEYWORD
nonn
AUTHOR
Franz Vrabec, Jan 20 2021
STATUS
approved