cp's OEIS Frontend

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

%I A263981 #29 Nov 17 2015 04:12:01
%S A263981 2,4,8,8,14,14,16,16,22,22,26,26,32,32,32,32,38,38,44,44,46,46,52,52,
%T A263981 58,58,58,58,62,62,64,64,74,74,74,74,82,82,82,82,86,86,92,92,94,94,
%U A263981 104,104,106,106,106,106,116,116,116,116,118,118,122,122,128,128
%N A263981 Least even k such that phi(k) >= n.
%C A263981 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.
%H A263981 Reza Akhtar, Anthony B. Evans, and Dan Pritikin, <a href="http://www.emis.de/journals/INTEGERS/papers/k54/k54.Abstract.html">Representation number of stars</a>, Integers 10 (2010), pp. 733-745. #A54
%H A263981 P. Erdős and A. B. Evans, <a href="http://www.renyi.hu/~p_erdos/1989-31.pdf">Representations of graphs and orthogonal Latin square graphs</a>, J. Graph Theory 13:5 (1989), pp. 593-595.
%F A263981 2n <= a(n) <= 2*A151800(n).
%e A263981 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.
%t A263981 Table[k = 2; While[EulerPhi@ k < n, k += 2]; k, {n, 62}] (* _Michael De Vlieger_, Nov 16 2015 *)
%o A263981 (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
%o A263981 (PARI) a(n)=my(k=2*n); while(eulerphi(k)<n, k+=2); k \\ _Charles R Greathouse IV_, Nov 02 2015
%Y A263981 Cf. A066169, A151800.
%K A263981 nonn
%O A263981 1,1
%A A263981 _Charles R Greathouse IV_, Oct 30 2015