The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A266266 Primes p such that p-1 = phi(p) = k*phi(p-k) for some number 1 <= k < p-1. 1
 5, 7, 11, 13, 17, 73, 257, 2593, 65537 (list; graph; refs; listen; history; text; internal format)
 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 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( 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)