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 A063903 #17 Jul 07 2022 20:26:05 %S A063903 1,3,14,42,248,594,744,4064,7668,12192,16775168,50325504,4294934528, %T A063903 12884803584,68719345664,206158036992 %N A063903 Numbers k such that ud(k)*phi(k) = sigma(k), ud(k) = A034444. %C A063903 From _Farideh Firoozbakht_, Mar 25 2007: (Start) %C A063903 (1) If 2^p-1 is prime (a Mersenne prime) then 2^(p-2)*(2^p-1) is in the sequence - the proof is easy. So 2^(A000043-2)*(2^A000043-1) is a subsequence of this sequence. %C A063903 (2) If k is in the sequence and 3 doesn't divide k then 3*k is in the sequence. Hence if 2^p-1 is a Mersenne prime greater than 3 then 3*2^(p-2)*(2^p-1) is in the sequence. %C A063903 Statement (2) is a special case of "If gcd(m,k)=1 and m & k are in the sequence then m*k is in the sequence (*)". (*) is correct because the three functions ud, phi & sigma are multiplicative. %C A063903 There is no further term up to 5.6*10^8. (End) %o A063903 (PARI) ud(n) = 2^omega(n); for(n=1,10^8, if(ud(n)*eulerphi(n)==sigma(n),print(n))) %Y A063903 Cf. A000043, A000668, A020492. %K A063903 nonn,more %O A063903 1,2 %A A063903 _Jason Earls_, Aug 30 2001 %E A063903 a(11) from _R. J. Mathar_, Nov 10 2006 %E A063903 a(12) from _Farideh Firoozbakht_, Mar 25 2007 %E A063903 a(13)-a(16) from _Donovan Johnson_, Mar 06 2013