1,1

If p is prime then the following two statements are true. I. 2p is in the sequence iff 2p+1 is composite (p isn't a Sophie Germain prime). II. 4p is in the sequence iff 2p+1 and 4p+1 are composite. - Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), 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

R. K. Guy, Unsolved Problems in Number Theory, B36.

T. D. Noe, Table of n, a(n) for n=1..10000

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

There are no values of m such that phi(m)=14, so 14 is a member of the sequence.

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[k] - 1)*(Prime[k]^l), {k, 70}, {l, 8}]}]] - Alonso Delarte (alonso.delarte(AT)gmail.com), Jun 10 2006

See A007617 for all values. Cf. A000010.

Cf. A005384.

Cf. A006093.

Adjacent sequences: A005274 A005275 A005276 this_sequence A005278 A005279 A005280

Sequence in context: A030786 A094163 A105583 this_sequence A079702 A082773 A112772

nonn

njas

More terms from Jud McCranie (j.mccranie(AT)comcast.net), Oct 13 2000