A226384 Numbers k such that rad(phi(k)) = phi(rad(k)).

1, 2, 3, 6, 7, 11, 12, 14, 22, 23, 24, 28, 31, 43, 44, 46, 47, 48, 56, 59, 62, 67, 71, 79, 83, 86, 88, 92, 94, 96, 103, 107, 112, 118, 124, 131, 134, 139, 142, 158, 166, 167, 172, 176, 179, 184, 188, 191, 192, 206, 211, 214, 223, 224, 227, 236, 239, 248, 262

Offset: 1

Author

José María Grau Ribas, Jun 05 2013

Keywords

• nonn

Comments

Numbers k such that A080400(k) = A173557(k). - Amiram Eldar, Apr 09 2020

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A007947, A080400, A173557.

Programs

Maple

with(numtheory):
rad:= n-> mul(i, i=factorset(n)):
a:= proc(n) option remember; local k; for k from 1+a(n-1)
      while phi(rad(k))<>rad(phi(k)) do od; k
    end: a(0):=0:
seq(a(n), n=1..80);  # Alois P. Heinz, Jun 07 2013

Mathematica

rad[n_] := Product[fa[n][[i, 1]], {i,
     Length[fa[n]]}]; fa = FactorInteger;
      Select[Range[500], rad[EulerPhi[#]] == EulerPhi[rad[#]] &]

PARI

is(n)=my(f=factor(n)); lcm(factor(eulerphi(f))[,1])==prod(i=1,#f~, f[i,1]-1) \\ Charles R Greathouse IV, Nov 13 2013