A069946 Numbers k such that phi(k) mod core(k) = 1 where core(k) is the squarefree part of k.

2, 12, 48, 60, 63, 75, 175, 192, 363, 405, 468, 704, 768, 816, 867, 891, 960, 980, 1008, 1020, 1587, 1875, 2023, 2107, 2331, 2475, 2523, 2527, 2800, 2835, 3072, 3075, 3185, 3332, 3757, 4100, 4335, 4477, 4851, 5043, 5780, 6171, 6292, 6627, 6727, 6877, 7220

Offset: 1

Author

Benoit Cloitre, Apr 27 2002

Keywords

• easy
• nonn

Comments

This sequence is infinite. For example, 3*4^k is a term for all k > 0, since core(3*4^k) = 3, phi(3*4^k) = 4^k and 4^k == 1 (mod 3). - Amiram Eldar, Sep 03 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002001, A007913.

Programs

Mathematica

core[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]); Select[Range[10^4], Mod[EulerPhi[#], core[#]] == 1 &] (* Amiram Eldar, Sep 03 2020 *)

PARI

for(n=1,15000,if(eulerphi(n)%core(n)==1,print1(n,",")))

Extensions

Name corrected by Amiram Eldar, Sep 05 2020