A071387 - OEIS

%I #24 Mar 28 2024 09:03:38

%S 0,2,8,32,40,48,396,704,72,216,144,1056,360,384,1320,240,9000,7128,

%T 480,1296,15936,3072,864,7344,720,4992,2016,6000,4752,3024,9984,1920,

%U 7560,22848,29160,3360,13248,27720,9072,9360,4032,4800,16896,3840,9504,23520,5040

%N Smallest number k for which the set of solutions to phi(x) = k has 2n-1 entries.

%H Amiram Eldar, <a href="/A071387/b071387.txt">Table of n, a(n) for n = 1..1000</a>

%H Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (see invphi.gp there).

%F a(n) = Min({x; Card(InvPhi(x)) = 2n-1}); a(1)=0 because of Carmichael conjecture.

%e For n = 7: 2n-1 = 13, a(7) = Min(InvPhi(13)) = Min({396,400,420,552,560,660}) = 396.

%o (PARI) a(n) = {if (n==1, return (0)); my(k=1); while(#invphi(k) != 2*n-1, k++); k;} \\ _Michel Marcus_, May 13 2020

%Y Cf. A000010 (phi), A014197, A058277, A063512, A071386, A071388, A071389.

%K nonn

%O 1,2

%A _Labos Elemer_, May 23 2002

%E a(12)-a(47) from _Donovan Johnson_, Jul 27 2011