A078893 -id:A078893 - cp's OEIS frontend

A078892 Numbers n such that phi(n) - 1 is prime, where phi is Euler's totient function (A000010).

5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 24, 25, 26, 27, 28, 30, 31, 33, 35, 36, 38, 39, 42, 43, 44, 45, 49, 50, 51, 52, 54, 56, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 77, 78, 80, 81, 84, 86, 90, 91, 92, 93, 95, 96, 98, 99, 102, 103, 104, 105, 109, 111, 112, 117

Offset: 1

Reinhard Zumkeller, Dec 12 2002

For all primes p: p is in the sequence iff p is the greater member of a twin prime pair (A006512), see A078893.

Union of A006512 and A078893. - Ray Chandler, May 26 2008

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000010, A000040, A008864, A109606, A006512, A039698, A072281, A078893.

[n: n in [1..200] | IsPrime(EulerPhi(n)-1)]; // Vincenzo Librandi, Aug 13 2013

Select[Range[200], PrimeQ[EulerPhi[#] - 1]&] (* Vincenzo Librandi, Aug 13 2013 *)

is(n)=isprime(eulerphi(n)-1) \\ Charles R Greathouse IV, Feb 21 2013

A068019 Composite n such that both 1 + phi(n) and -1 + phi(n) are primes, i.e., phi(n) is the middle term between twin primes (A014574).

Original entry on oeis.org

8, 9, 10, 12, 14, 18, 21, 26, 27, 28, 36, 38, 42, 49, 54, 62, 77, 86, 91, 93, 95, 98, 99, 111, 117, 122, 124, 133, 135, 146, 148, 152, 154, 171, 182, 186, 189, 190, 198, 206, 209, 216, 217, 218, 221, 222, 228, 234, 252, 266, 270, 278, 279, 287, 291, 297, 302

Offset: 1

Labos Elemer, Feb 08 2002

nonn

A072281 with the primes removed; intersection of A066071 and A078893. - Ray Chandler, May 26 2008

			n = 21, 26, 28, 36, 42 give phi(n)=12; the corresponding twin primes are {11,13}.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A000010, A000040, A014574, A066071, A072281, A078893, A068017.

Filtered([1..310],n->not IsPrime(n) and IsPrime(1+Phi(n)) and IsPrime(-1+Phi(n))); # Muniru A Asiru, Dec 08 2018

Do[s=-1+EulerPhi[n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]
(* Second program: *)
Select[Range[4, 302], And[CompositeQ@ #, AllTrue[EulerPhi@ # + {-1, 1}, PrimeQ]] &] (* Michael De Vlieger, Dec 08 2018 *)

isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ Michel Marcus, Dec 08 2018

cp's OEIS Frontend

A078892 Numbers n such that phi(n) - 1 is prime, where phi is Euler's totient function (A000010).

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