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 A308664 #44 May 31 2024 05:50:50
%S A308664 20,36,60,100,300
%N A308664 Numbers k such that tau(k) and phi(k) are the legs of a Pythagorean triple.
%C A308664 The sequence is finite since for all large enough n, we have tau(n) < n^(1/4) and phi(n) > n^(3/4) while, if x < y are the legs of a Pythagorean triangle, we always have y < x^2/2. - _Giovanni Resta_, Jul 27 2019
%C A308664 From Resta's inequality it can be deduced that phi(n) <= 2304. Then it's easy to see that the sequence is full. - _Max Alekseyev_, May 30 2024
%e A308664 60 is in this sequence because tau(60) = 12 and phi(60) = 16, legs of the Pythagorean triple {12, 16, 20} (12^2 + 16^2 = 20^2).
%t A308664 Select[Range[300], IntegerQ@Sqrt[DivisorSigma[0, #]^2 + EulerPhi[#]^2] &] (* _Amiram Eldar_, Jul 26 2019 *)
%o A308664 (PARI) for(i = 1, 2000, a = eulerphi(i); b = numdiv(i); if(issquare(a^2 + b^2), print1(i,", ")))
%Y A308664 Cf. A000005, A000010, A020488, A062516, A063469, A063470, A112954.
%K A308664 nonn,fini,full
%O A308664 1,1
%A A308664 _Antonio Roldán_, Jul 14 2019
%E A308664 "full" keyword added by _Max Alekseyev_, May 30 2024