A071387 Smallest number k for which the set of solutions to phi(x) = k has 2n-1 entries.

0, 2, 8, 32, 40, 48, 396, 704, 72, 216, 144, 1056, 360, 384, 1320, 240, 9000, 7128, 480, 1296, 15936, 3072, 864, 7344, 720, 4992, 2016, 6000, 4752, 3024, 9984, 1920, 7560, 22848, 29160, 3360, 13248, 27720, 9072, 9360, 4032, 4800, 16896, 3840, 9504, 23520, 5040

Offset: 1

Author

Labos Elemer, May 23 2002

Keywords

• nonn

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (see invphi.gp there).

Crossrefs

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

Programs

PARI

a(n) = {if (n==1, return (0)); my(k=1); while(#invphi(k) != 2*n-1, k++); k;} \\ Michel Marcus, May 13 2020

Formula

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

Extensions

a(12)-a(47) from Donovan Johnson, Jul 27 2011