cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A049198 #25 Mar 18 2025 07:33:00
%S A049198 4,9,18,49,98,121,242,529,961,1058,1849,1922,2209,3481,3698,4418,4489,
%T A049198 5041,6241,6889,6962,8978,10082,10609,11449,12482,13778,17161,19321,
%U A049198 21218,22898,27889,32041,34322,36481,38642,44521,49729,51529,55778,57121,64082,69169
%N A049198 Numbers that are not squarefree and whose Euler totient function is squarefree.
%C A049198 Numbers k such that abs(mu(phi(k))) = 1 and abs(mu(k)) = 0.
%C A049198 Contains all the squares p^2 of primes p such that p-1 is squarefree (A039787). - _Amiram Eldar_, Mar 18 2025
%H A049198 Donovan Johnson, <a href="/A049198/b049198.txt">Table of n, a(n) for n = 1..5000</a>
%e A049198 a(27) = 13778 = 2*83*83 is divisible by a square, but phi(13778) = 6806 = 2*41*83 is squarefree.
%t A049198 Select[Range[70000], Abs[ MoebiusMu[ EulerPhi[ # ] ] ] == 1 && Abs[ MoebiusMu[ # ] ] == 0 &]
%o A049198 (PARI) isok(k)=!issquarefree(k) && issquarefree(eulerphi(k)) \\ _Donovan Johnson_, Jun 20 2012
%Y A049198 Intersection of A049149 and A013929.
%Y A049198 Cf. A000010, A005117, A008683, A039787, A049199.
%K A049198 nonn
%O A049198 1,1
%A A049198 _Labos Elemer_