[seqfan] A question about A005277 terms (Nontotients: even n such that phi(m) = n has no solution)

Eduard Cifre Urusenar at hotmail.com
Mon Apr 25 13:17:21 CEST 2022

Hello everybody. In the comments section of nontotients numbers (A005277), 4 ways to find nontotient numbers are described in it:

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<https://oeis.org/wiki/User: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<https://oeis.org/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.

54 meets the conditions: b = 53 congruent 1 (mod 4), k = 1 and 55 = 5 · 11, however it's no included in the serie. Am I misunderstanding something about nontotient numbers? How can I check that does not exists n such phi(n) = 54? Thanks for your attention.

More information about the SeqFan mailing list