A069236 Integers m, not a perfect square, such that the squarefree part of m divides phi(m).

8, 18, 27, 32, 50, 54, 72, 98, 108, 125, 128, 147, 162, 200, 216, 242, 243, 250, 288, 294, 338, 343, 392, 432, 450, 486, 500, 507, 512, 578, 588, 605, 648, 675, 686, 722, 800, 864, 882, 968, 972, 1000, 1014, 1029, 1058, 1083, 1125, 1152, 1176, 1210, 1250

Offset

1,1

Links

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

Example

108 is not a square, phi(108)=36, 3 is the squarefree part of 108 and 3 divides 36. Hence a(9)=108 is in the sequence.

Mathematica

f[p_, e_] := (p - 1)*p^((e - 1) - Mod[e, 2]); q[n_] := ! AllTrue[(fct = FactorInteger[n])[[;; , 2]], EvenQ] && IntegerQ[Times @@ f @@@ fct]; Select[Range[2, 1250], q] (* Amiram Eldar, Mar 09 2021 *)

Prog

(PARI) isok(m) = !issquare(m) && !(eulerphi(m) % core(m)); \\ Michel Marcus, Nov 30 2020

Crossrefs

Cf. A000010, A000037, A007913.

Sequence in context: A298161 A195419 A110188 * A187101 A051370 A290614

Adjacent sequences: A069233 A069234 A069235 * A069237 A069238 A069239

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 13 2002

Extensions

Name edited by Michel Marcus, Nov 30 2020

Status

approved