A340762 Numbers k such that iterations of phi(k), phi(phi(k)), ... end in ... 4, 2, 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
Offset: 1
Keywords
Examples
11 is in the list because phi(phi(11)) = phi(10) = 4.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- 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.
Programs
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Maple
filter:= proc(n) option remember; if n < 4 then false elif n = 4 then true else procname(numtheory:-phi(n)) fi end proc: select(filter, [$4..100]); # Robert Israel, Dec 23 2021
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Mathematica
Select[Range[4, 72], FixedPointList[EulerPhi, #][[-4]] == 4 &] (* Amiram Eldar, Jan 27 2021 *)
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PARI
isok(k) = if (k>=4, while((k!=6) && (k!=4), k=eulerphi(k))); k == 4; \\ Michel Marcus, Feb 01 2021
Comments