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 A244439 #25 Jun 08 2020 17:09:11
%S A244439 5,55,56,123,135,147,175,304,351,644,1015,2464,19304,61131,162524,
%T A244439 476671,567644,712724,801944,2435488,3346399,3885056,4555999,8085560,
%U A244439 8369360,12516692,22702119,29628800,83884031,83994624,84789247,354812535,860616295,1091535704
%N A244439 Numbers n such that phi(n)*sigma(n) = phi(n+1)*sigma(n+1).
%C A244439 Since both numbers 55 and 56 are in the sequence we have sigma(55)*phi(55) = sigma(56)*phi(56) = sigma(57)*phi(57). It seems that 56 is the only number n which has the nice property sigma(n-1)*phi(n-1) = sigma(n)*phi(n) = sigma(n+1)*phi(n+1).
%C A244439 Up to n < 6*10^11 the similar equation phi(n)*sigma(n+1) = phi(n+1)*sigma(n) is satisfied only by n = 696003. - _Giovanni Resta_, Jun 08 2020
%H A244439 Giovanni Resta, <a href="/A244439/b244439.txt">Table of n, a(n) for n = 1..52</a> (terms < 10^13, first 40 terms from Jens Kruse Andersen)
%e A244439 5 is in the sequence because sigma(5)*phi(5) = sigma(6)*phi(6) = 24.
%e A244439 55 is in the sequence because sigma(55)*phi(55) = sigma(56)*phi(56) = 2880.
%p A244439 with(numtheory): A244439:=n->`if`(phi(n)*sigma(n) = phi(n+1)*sigma(n+1), n, NULL): seq(A244439(n), n=1..10^4); # _Wesley Ivan Hurt_, Aug 16 2014
%t A244439 Select[Range[10^5], Equal @@ (EulerPhi[{#, # + 1}] DivisorSigma[1, {#, # + 1}]) &] (* _Giovanni Resta_, Jun 08 2020 *)
%o A244439 (PARI)
%o A244439 for(n=1,10^6,s=eulerphi(n)*sigma(n);if(s==eulerphi(n+1)*sigma(n+1),print1(n,", "))) \\ _Derek Orr_, Aug 14 2014
%Y A244439 Cf. A000010, A000203, A145749.
%K A244439 nonn
%O A244439 1,1
%A A244439 _Farideh Firoozbakht_, Aug 14 2014
%E A244439 More terms from _Jens Kruse Andersen_, Aug 16 2014