A068560 - OEIS

%I #34 May 31 2024 05:51:17

%S 1,5,34,63,76,128,136,170,315,364,380,444,640,680,972,1820,1824,1836,

%T 2142,2220,4788,4860,6000,8064,8568,8736,9120,9180,10710,23940,40320,

%U 42840,43680

%N Numbers k such that phi(k) = tau(k)^2.

%C This sequence is finite because phi(k) >= sqrt(k) for all k >= 6, and for any e > 0, tau(k) < k^e for k large enough. Choosing e=1/4 gives tau(k)^2 < sqrt(k) <= phi(k). It remains unknown, however, if this sequence is full. - _Nathaniel Johnston_, Apr 28 2011

%C It can be shown that tau(k) <= 120 and the sequence is complete. - _Max Alekseyev_, May 30 2024

%e a(2) = A107655(2) = 5.

%t Do[If[EulerPhi[n] == DivisorSigma[0, n]^2, Print[n]], {n, 10^5}] (* _Ryan Propper_, Jun 09 2006 *)

%t Select[Range[10^5], EulerPhi[#] == DivisorSigma[0, #]^2 &] (* _Alonso del Arte_, Aug 25 2011 *)

%Y Cf. A039770, A068559, A107655, A114063.

%K fini,full,nonn

%O 1,2

%A _Benoit Cloitre_, Mar 25 2002

%E More terms from _Ryan Propper_, Jun 09 2006

%E "full" keyword added by _Max Alekseyev_, May 30 2024