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 A005277 Nontotients: even numbers k such that phi(m) = k has no solution. (Formerly M4927) 92
 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, 302, 304, 308, 314, 318 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is prime then the following two statements are true. I. 2p is in the sequence iff 2p+1 is composite (p is not a Sophie Germain prime). II. 4p is in the sequence iff 2p+1 and 4p+1 are composite. - Farideh Firoozbakht, Dec 30 2005 Another subset of nontotients consists of the numbers j^2 + 1 such that j^2 + 2 is composite. These numbers j are given in A106571. Similarly, let b be 3 or a number such that b == 1 (mod 4). For any j > 0 such that b^j + 2 is composite, b^j + 1 is a nontotient. - T. D. Noe, Sep 13 2007 The Firoozbakht comment can be generalized: Observe that if k is a nontotient and 2k+1 is composite, then 2k is also a nontotient. See A057192 and A076336 for a connection to Sierpiński numbers. This shows that 271129*2^j is a nontotient for all j > 0. - T. D. Noe, Sep 13 2007 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, B36. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..29750 (terms 1..10000 from T. D. Noe). Lambert A'Campo, Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible L-adic Galois Representation, arXiv:2006.06737 [math.NT], 2020. Matteo Caorsi and Sergio Cecotti, Geometric classification of 4d N=2 SCFTs, arXiv:1801.04542 [hep-th], 2018. K. Ford, S. Konyagin, and C. Pomerance, Residue classes free of values of Euler's function, arXiv:2005.01078 [math.NT] (1999). L. Havelock, A Few Observations on Totient and Cototient Valence. Eric Weisstein's World of Mathematics, Nontotient. Wikipedia, Nontotient Robert G. Wilson v, Letter to N. J. A. Sloane, Jul. 1992 FORMULA a(n) = 2*A079695(n). - R. J. Mathar, Sep 29 2021 {k: k even and A014197(k) = 0}. - R. J. Mathar, Sep 29 2021 EXAMPLE There are no values of m such that phi(m)=14, so 14 is a term of the sequence. MAPLE A005277 := n -> if type(n, even) and invphi(n)=[] then n fi: seq(A005277(i), i=1..318); # Peter Luschny, Jun 26 2011 MATHEMATICA searchMax = 320; phiAnsYldList = Table[0, {searchMax}]; Do[phiAns = EulerPhi[m]; If[phiAns <= searchMax, phiAnsYldList[[phiAns]]++ ], {m, 1, searchMax^2}]; Select[Range[searchMax], EvenQ[ # ] && (phiAnsYldList[[ # ]] == 0) &] (* Alonso del Arte, Sep 07 2004 *) totientQ[m_] := Select[ Range[m +1, 2m*Product[(1 - 1/(k*Log[k]))^(-1), {k, 2, DivisorSigma[0, m]}]], EulerPhi[#] == m &, 1] != {}; (* after Jean-François Alcover, May 23 2011 in A002202 *) Select[2 Range@160, ! totientQ@# &] (* Robert G. Wilson v, Mar 20 2023 *) PROG (Haskell) a005277 n = a005277_list !! (n-1) a005277_list = filter even a007617_list -- Reinhard Zumkeller, Nov 22 2015 (PARI) is(n)=n%2==0 && !istotient(n) \\ Charles R Greathouse IV, Mar 04 2017 (Magma) [n: n in [2..400 by 2] | #EulerPhiInverse(n) eq 0]; // Marius A. Burtea, Sep 08 2019 CROSSREFS See A007617 for all numbers k (odd or even) such that phi(m) = k has no solution. All even numbers not in A002202. Cf. A000010. Cf. A005384, A006093. Sequence in context: A134837 A105583 A323030 * A079702 A235688 A176274 Adjacent sequences: A005274 A005275 A005276 * A005278 A005279 A005280 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Jud McCranie, Oct 13 2000 STATUS approved

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Last modified September 25 15:05 EDT 2023. Contains 365648 sequences. (Running on oeis4.)