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%I M4688
%S 10,26,34,50,52,58,86,100,116,122,130,134,146,154,170,172,186,202,206,
%T 218,222,232,244,260,266,268,274,290,292,298,310,326,340,344,346,362,
%U 366,372,386,394,404,412,436,466,470,474,482,490,518,520
%N Noncototients: n such that x - phi(x) = n has no solution.
%C 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_, Mar 03 2002
%D 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]
%D R. K. Guy, Unsolved Problems in Number Theory, B36.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe and Donovan Johnson, <a href="/A005278/b005278.txt">Table of n, a(n) for n = 1..10000</a> (first 963 terms from T. D. Noe)
%H C. Pomerance and H.-S. Yang, <a href="http://www.math.dartmouth.edu/~carlp/uupaper3.pdf">On untouchable numbers and related problems</a>, 2012
%H C. Pomerance and H.-S. Yang, <a href="http://www.math.dartmouth.edu/~carlp/uupaper6.pdf">Variant of a theorem of Erdos on the sum-of-proper-divisors function</a>, 2012
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Noncototient.html">Noncototient</a>
%t 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[#]&] (* Jean-François Alcover, Jul 20 2011 *)
%Y Cf. A006093, A126887. Complement of A051953.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_.
%E More terms from _Jud McCranie_ 1/97.
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