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A007617
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Values not in range of Euler phi function.
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41
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3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 81, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98, 99, 101, 103, 105, 107
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OFFSET
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1,1
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COMMENTS
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Nontotient numbers.
All odd numbers > 2 are in the sequence.
The even numbers of the sequence are in A005277.
The asymptotic density of this sequence is 1. - Amiram Eldar, Mar 26 2021
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REFERENCES
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Richard K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, section B36, page 138-142.
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LINKS
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Zhang Ming-Zhi, On nontotients, J. Number Theory, Vol. 43, No. 2 (1993), pp. 168-173.
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FORMULA
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EXAMPLE
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There are no solutions to phi(m)=14, so 14 is a member of the sequence.
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MAPLE
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MATHEMATICA
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inversePhi[m_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m*Times @@ (p/(p - 1)); n = m; nn = {}; While[n <= nmax, If[EulerPhi[n] == m, AppendTo[nn, n]]; n++]; nn]; Select[Range[107], inversePhi[#] == {} &] (* Jean-François Alcover, Jan 03 2012 *)
Select[Range[107], invphi[#] == {}&] (* Jean-François Alcover, Mar 19 2019, using Maxim Rytin's much faster 'invphi' program *)
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PROG
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(Haskell)
import Data.List.Ordered (minus)
a007617 n = a007617_list !! (n-1)
a007617_list = [1..] `minus` a002202_list
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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