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 A051445 #20 Dec 12 2024 17:18:24 %S A051445 3,5,7,15,11,13,0,17,19,25,23,35,0,29,31,51,0,37,0,41,43,69,47,65,0, %T A051445 53,81,87,59,61,0,85,67,0,71,73,0,0,79,123,83,129,0,89,0,141,0,97,0, %U A051445 101,103,159,107,109,121,113,0,177,0,143,0,0,127,255,131,161,0,137 %N A051445 Smallest k such that phi(k) = 2n, or 0 if there is no such k. %C A051445 The zero values are easy to prove because of the bounds on the phi function. %H A051445 T. D. Noe, <a href="/A051445/b051445.txt">Table of n, a(n) for n = 1..10000</a> %F A051445 a(10^n/2) = A072075(n). - _R. J. Mathar_, Dec 12 2024 %F A051445 a(A079695(n)) = 0. - _David A. Corneth_, Dec 12 2024 %e A051445 a(4) = 15 as phi(15) = 2*4 and no k < 15 has phi(k) = 2*4. %o A051445 (PARI) a(n)=n+=n;for(k=n+1, solve(x=n,if(n<20,99,5*n*log(log(n))), x/(exp(Euler)*log(log(x))+3/log(log(x)))-n), if(eulerphi(k)==n,return(k))); 0 \\ _Charles R Greathouse IV_, Dec 19 2011 %Y A051445 Cf. A002181, A072075, A079695. For records see A132012, A132115. %K A051445 nonn %O A051445 1,1 %A A051445 _Jud McCranie_