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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 (list; graph; refs; listen; history; text; internal format)
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 phi-tree, Amer. Math. Monthly, Vol. 93, No. 7 (August-September 1986), pp. 552-554.

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

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Last modified June 17 17:41 EDT 2021. Contains 345085 sequences. (Running on oeis4.)