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A005277 Nontotients: even n such that phi(m) = n has no solution.
(Formerly M4927)
55
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 Sierpinski 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

K. Ford, S. Konyagin, C. Pomerance, Residue classes free of values of Euler's function (1999). [From R. J. Mathar, Mar 15 2010]

L. Havelock, A Few Observations on Totient and Cototient Valence.

Eric Weisstein's World of Mathematics, Nontotient.

Wikipedia, Nontotient

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 *)

CROSSREFS

See A007617 for all values. Cf. A000010.

Cf. A005384.

Cf. A006093.

Sequence in context: A094163 A134837 A105583 * A079702 A235688 A176274

Adjacent sequences:  A005274 A005275 A005276 * A005278 A005279 A005280

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Jud McCranie, Oct 13 2000

STATUS

approved

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Last modified December 21 04:58 EST 2014. Contains 252293 sequences.