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

1,1

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002001, A007913.

Sequence in context: A302447 A319763 A320684 * A176684 A216152 A048501

Adjacent sequences: A069943 A069944 A069945 * A069947 A069948 A069949

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 27 2002

Extensions

Name corrected by Amiram Eldar, Sep 05 2020

Status

approved