

A340762


Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 4, 2, 1.


1



4, 5, 8, 10, 11, 12, 13, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72
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OFFSET

1,1


COMMENTS

Infinite set (see reference).


LINKS

Table of n, a(n) for n=1..60.
Eliot T. Jacobson and Alan E. Parks, Infinite branches of the phitree, Amer. Math. Monthly, Vol. 93, No. 7 (AugustSeptember 1986), pp. 552554.
Keith Matthews, Solving phi(x)=n, where phi(x) is Euler's totient function.


EXAMPLE

11 is in the list because phi(phi(11)))) = phi(10) = 4.


MATHEMATICA

Select[Range[4, 72], FixedPointList[EulerPhi, #][[4]] == 4 &] (* Amiram Eldar, Jan 27 2021 *)


PROG

(PARI) isok(k) = if (k>=4, while((k!=6) && (k!=4), k=eulerphi(k))); k == 4; \\ Michel Marcus, Feb 01 2021


CROSSREFS

Cf. A000010, A340765 (complement relative to {n>=4}).
Cf. A003434, A032358, A049108.
Sequence in context: A268128 A064394 A141220 * A092022 A190200 A162902
Adjacent sequences: A340759 A340760 A340761 * A340763 A340764 A340765


KEYWORD

nonn


AUTHOR

Franz Vrabec, Jan 20 2021


STATUS

approved



