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 A005277 Nontotients: even n such that phi(m) = n has no solution. (Formerly M4927) 59
 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 n^2 + 1 such that n^2 + 2 is composite. These n are given in A106571. Similarly, let b be 3 or a number such that b=1 (mod 4). For any k > 0 such that b^k + 2 is composite, b^k + 1 is a nontotient. - T. D. Noe, Sep 13 2007 The Firoozbakht comment can be generalized: Observe that if n is a nontotient and 2n+1 is composite, then 2n is also a nontotient. See A057192 and A076336 for a connection to Sierpiński numbers. This shows that 271129*2^k is a nontotient for all k > 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 T. D. Noe, Table of n, a(n) for n = 1..10000 Matteo Caorsi, Sergio Cecotti, Geometric classification of 4d N=2 SCFTs, arXiv:1801.04542 [hep-th], 2018. K. Ford, S. Konyagin, C. Pomerance, Residue classes free of values of Euler's function (1999). L. Havelock, A Few Observations on Totient and Cototient Valence. [Broken link] Eric Weisstein's World of Mathematics, Nontotient. Wikipedia, Nontotient R. G. Wilson, V, Letter to N. J. A. Sloane, Jul. 1992 EXAMPLE There are no values of m such that phi(m)=14, so 14 is a member 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 *) Complement[2*Range[159], Flatten[{Table[(Prime[i] - 1)*(Prime[j] - 1), {i, 70}, {j, 70}], Table[(Prime[i] - 1)*(Prime[j]^i), {i, 70}, {j, 8}]}]] (* Alonso del Arte, Jun 10 2006 *) 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 CROSSREFS See A007617 for all values. All even numbers not in A002202. Cf. A000010. Cf. A005384, A006093. Sequence in context: A094163 A134837 A105583 * A079702 A235688 A176274 Adjacent sequences:  A005274 A005275 A005276 * A005278 A005279 A005280 KEYWORD nonn AUTHOR EXTENSIONS More terms from Jud McCranie, Oct 13 2000 STATUS approved

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Last modified December 9 17:51 EST 2018. Contains 318023 sequences. (Running on oeis4.)