A049198 Numbers that are not squarefree and whose Euler totient function is squarefree.

4, 9, 18, 49, 98, 121, 242, 529, 961, 1058, 1849, 1922, 2209, 3481, 3698, 4418, 4489, 5041, 6241, 6889, 6962, 8978, 10082, 10609, 11449, 12482, 13778, 17161, 19321, 21218, 22898, 27889, 32041, 34322, 36481, 38642, 44521, 49729, 51529, 55778, 57121, 64082, 69169

Offset

1,1

Comments

Numbers k such that abs(mu(phi(k))) = 1 and abs(mu(k)) = 0.

Contains all the squares p^2 of primes p such that p-1 is squarefree (A039787). - Amiram Eldar, Mar 18 2025

Links

Donovan Johnson, Table of n, a(n) for n = 1..5000

Example

a(27) = 13778 = 2*83*83 is divisible by a square, but phi(13778) = 6806 = 2*41*83 is squarefree.

Mathematica

Select[Range[70000], Abs[ MoebiusMu[ EulerPhi[ # ] ] ] == 1 && Abs[ MoebiusMu[ # ] ] == 0 &]

Prog

(PARI) isok(k)=!issquarefree(k) && issquarefree(eulerphi(k)) \\ Donovan Johnson, Jun 20 2012

Crossrefs

Intersection of A049149 and A013929.

Cf. A000010, A005117, A008683, A039787, A049199.

Sequence in context: A261983 A074896 A015713 * A146303 A344999 A203205

Adjacent sequences: A049195 A049196 A049197 * A049199 A049200 A049201

Keyword

nonn

Author

Labos Elemer

Status

approved