Search: id:A005277
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%I A005277 M4927
%S A005277 14,26,34,38,50,62,68,74,76,86,90,94,98,114,118,122,124,134,142,146,
%T A005277 152,154,158,170,174,182,186,188,194,202,206,214,218,230,234,236,242,
%U A005277 244,246,248,254,258,266,274,278,284,286,290,298,302,304,308,314,318
%N A005277 Nontotients: even n such that phi(m) = n has no solution.
%C A005277 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
%C A005277 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
%C A005277 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
%D A005277 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005277 R. K. Guy, Unsolved Problems in Number Theory, B36.
%H A005277 T. D. Noe, <a href="b005277.txt">Table of n, a(n) for n=1..10000</a>
%H A005277 L. Havelock, <a href="http://aux.planetmath.org/files/papers/335/C:TempObsTotientCototientValence.pdf">
               A Few Observations on Totient and Cototient Valence</a>.
%H A005277 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Nontotient.html">Link to a section of The World of Mathematics.</
               a>
%H A005277 Wikipedia, <a href="http://en.wikipedia.org/wiki/Nontotient">Nontotient</
               a>
%e A005277 There are no values of m such that phi(m)=14, so 14 is a member of the 
               sequence.
%t A005277 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)
%t A005277 Complement[2*Range[159], Flatten[{Table[(Prime[i] - 1)*(Prime[j] - 1), 
               {i, 70}, {j, 70}], Table[(Prime[k] - 1)*(Prime[k]^l), {k, 70}, {l, 
               8}]}]] - Alonso Delarte (alonso.delarte(AT)gmail.com), Jun 10 2006
%Y A005277 See A007617 for all values. Cf. A000010.
%Y A005277 Cf. A005384.
%Y A005277 Cf. A006093.
%Y A005277 Sequence in context: A094163 A134837 A105583 this_sequence A079702 A082773 
               A112772
%Y A005277 Adjacent sequences: A005274 A005275 A005276 this_sequence A005278 A005279 
               A005280
%K A005277 nonn
%O A005277 1,1
%A A005277 N. J. A. Sloane (njas(AT)research.att.com).
%E A005277 More terms from Jud McCranie (j.mccranie(AT)comcast.net), Oct 13 2000

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