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.
%I A068560 #34 May 31 2024 05:51:17
%S A068560 1,5,34,63,76,128,136,170,315,364,380,444,640,680,972,1820,1824,1836,
%T A068560 2142,2220,4788,4860,6000,8064,8568,8736,9120,9180,10710,23940,40320,
%U A068560 42840,43680
%N A068560 Numbers k such that phi(k) = tau(k)^2.
%C A068560 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 A068560 It can be shown that tau(k) <= 120 and the sequence is complete. - _Max Alekseyev_, May 30 2024
%e A068560 a(2) = A107655(2) = 5.
%t A068560 Do[If[EulerPhi[n] == DivisorSigma[0, n]^2, Print[n]], {n, 10^5}] (* _Ryan Propper_, Jun 09 2006 *)
%t A068560 Select[Range[10^5], EulerPhi[#] == DivisorSigma[0, #]^2 &] (* _Alonso del Arte_, Aug 25 2011 *)
%Y A068560 Cf. A039770, A068559, A107655, A114063.
%K A068560 fini,full,nonn
%O A068560 1,2
%A A068560 _Benoit Cloitre_, Mar 25 2002
%E A068560 More terms from _Ryan Propper_, Jun 09 2006
%E A068560 "full" keyword added by _Max Alekseyev_, May 30 2024