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A005277
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Nontotients: even n such that phi(m) = n has no solution.
(Formerly M4927)
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55
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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; internal format)
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OFFSET
| 1,1
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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 (mymontain(AT)yahoo.com), 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 Sierpinski numbers. This shows that 271129*2^k is a nontotient for all k>0. - T. D. Noe, Sep 13 2007
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
K. Ford, S. Konyagin, C. Pomerance, Residue classes free of values of Euler's function (1999). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 15 2010]
L. Havelock, A Few Observations on Totient and Cototient Valence.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Nontotient
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EXAMPLE
| There are no values of m such that phi(m)=14, so 14 is a member of the sequence.
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MAPLE
| A005277 := n -> if type(n, even) and invphi(n)=[] then n fi: seq(A005277(i), i=1..318); # Peter Luschny, Jun 26 2011
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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 Delarte (alonso.delarte(AT)gmail.com), 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 Delarte (alonso.delarte(AT)gmail.com), Jun 10 2006 *)
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CROSSREFS
| See A007617 for all values. Cf. A000010.
Cf. A005384.
Cf. A006093.
Sequence in context: A094163 A134837 A105583 * A079702 A176274 A191992
Adjacent sequences: A005274 A005275 A005276 * A005278 A005279 A005280
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Oct 13 2000
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