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 A068559 #28 May 31 2024 05:53:01 %S A068559 1,85,333,436,1542,1875,2907,3285,3488,3796,5196,10280,17532,17776, %T A068559 20080,21250,28305,30368,30555,32708,34748,35308,36860,37060,41544, %U A068559 41568,43068,44004,45162,48468,51930,81324,98304,98688,104856,131070 %N A068559 Numbers m such that phi(m) = tau(m)^3. %C A068559 For all large enough k, we have tau(k) < k^(1/4) and phi(k) > k^(3/4). Hence, tau(k)^3 < k^(3/4) < phi(k), implying that this sequence is finite. In fact, the sequence consists of 614 terms. - _Max Alekseyev_, May 30 2024 %H A068559 Max Alekseyev, <a href="/A068559/b068559.txt">Table of n, a(n) for n = 1..614</a> (first 470 terms from Enrique Pérez Herrero) %e A068559 a(2) = A107655(3) = 85. %t A068559 Select[Range[132000],EulerPhi[#]==DivisorSigma[0,#]^3&] (* _Harvey P. Dale_, Dec 28 2022 *) %o A068559 (PARI) isok(m) = eulerphi(m) == numdiv(m)^3; \\ _Michel Marcus_, Oct 18 2019 %Y A068559 Subsequence of A039771. - _Enrique Pérez Herrero_, Aug 29 2010 %Y A068559 Cf. A020488, A068560, A107655, A114063. %K A068559 nonn,fini,full %O A068559 1,2 %A A068559 _Benoit Cloitre_, Mar 25 2002