A143423 Least even number k such that phi(k) = n, where n runs through the values (A002202) taken by phi.

2, 4, 8, 14, 16, 22, 26, 32, 38, 44, 46, 52, 58, 62, 64, 74, 82, 86, 92, 94, 104, 106, 162, 116, 118, 122, 128, 134, 142, 146, 158, 164, 166, 172, 178, 188, 194, 202, 206, 212, 214, 218, 242, 226, 236, 244, 254, 256, 262, 268, 274, 278, 284, 292, 298, 302, 314

Offset: 1

Author

T. D. Noe, Aug 14 2008

Keywords

• nonn

Comments

Such an even number always exists.

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• Maxim Rytin, Finding the Inverse of Euler Totient Function (1999).

Crossrefs

Cf. A002181 (least k such that phi(k)=n), A006511 (largest k such that phi(k)=n).

Programs

Maple

f:= proc(m) local L;
      L:= numtheory:-invphi(m);
      if L = [] then NULL
      else min(select(type,L,even))
      fi
end proc:
map(f, [1,seq(2*k,k=1..1000)]); # Robert Israel, Oct 07 2015

Mathematica

f[m_] := Module[{L}, L = invphi[m]; If[L == {}, Nothing, Min[Select[L, EvenQ]]]];
f /@ Join [{1}, 2 Range[1000]] (* Jean-François Alcover, Aug 28 2020, using Maxim Rytin's invphi function *)