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

Author

Labos Elemer

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Intersection of A049149 and A013929.

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

Programs

Mathematica

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

PARI

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