A263981 Least even k such that phi(k) >= n.

2, 4, 8, 8, 14, 14, 16, 16, 22, 22, 26, 26, 32, 32, 32, 32, 38, 38, 44, 44, 46, 46, 52, 52, 58, 58, 58, 58, 62, 62, 64, 64, 74, 74, 74, 74, 82, 82, 82, 82, 86, 86, 92, 92, 94, 94, 104, 104, 106, 106, 106, 106, 116, 116, 116, 116, 118, 118, 122, 122, 128, 128

Offset: 1

Author

Charles R Greathouse IV, Oct 30 2015

Keywords

• nonn

Comments

Representation number of the bipartite graph K_{1,n} (the n-pointed star graph), see Akhtar, Evans, & Pritikin. A graph G is said to have a representation mod r if each of its vertices can be given a unique label mod r such that two vertices are adjacent if and only if the difference of their representation numbers is coprime to r. The representation number of G is the least r for which G has a representation mod r, see Erdős & Evans.

Examples

			The star graph with center C and other points P1, P2, P3 can be labeled with C = 0 mod 8, P1 = 1 mod 8, P2 = 3 mod 8, and P3 = 5 mod 8 so that two points are adjacent iff their difference is odd (=coprime to 8), so a(3) <= 8.
		

Links

• Reza Akhtar, Anthony B. Evans, and Dan Pritikin, Representation number of stars, Integers 10 (2010), pp. 733-745. #A54
• P. Erdős and A. B. Evans, Representations of graphs and orthogonal Latin square graphs, J. Graph Theory 13:5 (1989), pp. 593-595.

Crossrefs

Cf. A066169, A151800.

Programs

Mathematica

Table[k = 2; While[EulerPhi@ k < n, k += 2]; k, {n, 62}] (* Michael De Vlieger, Nov 16 2015 *)

PARI

/* oo = 10^10; */ /* uncomment for earlier pari versions */ a(n)=forstep(k=2*n,oo,2,if(eulerphi(k)>=n,return(k))) \\ Charles R Greathouse IV, Oct 30 2015

PARI

a(n)=my(k=2*n); while(eulerphi(k)Charles R Greathouse IV, Nov 02 2015

Formula

2n <= a(n) <= 2*A151800(n).