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A005278
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Noncototients: n such that x-phi(x)=n has no solution.
(Formerly M4688)
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20
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10, 26, 34, 50, 52, 58, 86, 100, 116, 122, 130, 134, 146, 154, 170, 172, 186, 202, 206, 218, 222, 232, 244, 260, 266, 268, 274, 290, 292, 298, 310, 326, 340, 344, 346, 362, 366, 372, 386, 394, 404, 412, 436, 466, 470, 474, 482, 490, 518, 520
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2002
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REFERENCES
| J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. Math., 68 (1995), 55-58. [Shows that this sequence is infinite. - Labos E. (labos(AT)ana.sote.hu), Dec 21 1999]
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..963
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
| nmax = 520; cototientQ[n_?EvenQ] := (x = n; While[test = x - EulerPhi[x] == n ; Not[test || x > 2*nmax], x++]; test); cototientQ[n_?OddQ] = True; Select[Range[nmax], !cototientQ[#]&] (* From Jean-François Alcover, Jul 20 2011 *)
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CROSSREFS
| Cf. A006093, A126887. Complement of A051953.
Sequence in context: A043342 A023715 A045143 * A157075 A045039 A080059
Adjacent sequences: A005275 A005276 A005277 * A005279 A005280 A005281
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KEYWORD
| nonn,nice
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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) 1/97.
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