A266266 Primes p such that p-1 = phi(p) = k*phi(p-k) for some number 1 <= k < p-1.

5, 7, 11, 13, 17, 73, 257, 2593, 65537

Offset

1,1

Comments

Corresponding values of numbers k: 2, 3, 5, 3, 2, 3, 2, 3, 2, ...

83623937 is also a term of this sequence (with k = 2).

For all primes p we have: phi(p) = k*phi(p-k) if k = p - 1.

Primes from A266267.

The first 4 known Fermat primes > 3 from A019434 are in sequence.

Links

Table of n, a(n) for n=1..9.

Example

17 is in the sequence because phi(17) = 16 = 2*phi(15) = 2*8.

Mathematica

Select[Prime@ Range@ 500, Function[p, AnyTrue[Range[p - 2], p - 1 == # EulerPhi[p - #] &]]] (* Michael De Vlieger, Jan 09 2016, Version 10 *)

Prog

(Magma) Set(Sort([[n: k in [1..n-2] | IsPrime(n) and EulerPhi(n) eq k*EulerPhi(n-k)]: n in [1..10000]]))
(Magma) Set(Sort([5] cat [n: n in [6..100000], k in [1..5] | IsPrime(n) and EulerPhi(n) eq k*EulerPhi(n-k)]))
(PARI) listp(nn) = {forprime(p=2, nn, for (k=1, p-2, if (eulerphi(p) == k*eulerphi(p-k), print1(p, ", "); break)); ); } \\ Michel Marcus, Dec 27 2015

Crossrefs

Cf. A000010, A019434, A266267.

Sequence in context: A317250 A007529 A287956 * A246463 A314297 A108409

Adjacent sequences: A266263 A266264 A266265 * A266267 A266268 A266269

Keyword

nonn,more

Author

Jaroslav Krizek, Dec 26 2015

Status

approved