A268342 Number of edges in the unitary addition Cayley graph Gn.

0, 2, 2, 8, 8, 12, 18, 32, 24, 40, 50, 48, 72, 84, 56, 128, 128, 108, 162, 160, 120, 220, 242, 192, 240, 312, 234, 336, 392, 240, 450, 512, 320, 544, 408, 432, 648, 684, 456, 640, 800, 504, 882, 880, 528, 1012, 1058, 768, 1008, 1000, 800, 1248, 1352, 972, 1080, 1344

Offset

1,2

Comments

For n>1, the unitary addition Cayley graph Gn is the graph whose vertices are Z/nZ and where 2 vertices x and y are adjacent if x+y is a unit in Z/nZ.

Links

Table of n, a(n) for n=1..56.

Formula

a(n) = n*phi(n) if n is even, (n-1)*phi(n)/2 if n is odd.

Mathematica

Table[If[EvenQ@ n, n EulerPhi[n], (n - 1) EulerPhi[n]/2], {n, 56}] (* Michael De Vlieger, Feb 02 2016 *)

Prog

(PARI) a(n) = if (n % 2, eulerphi(n)*(n-1)/2, eulerphi(n)*n);
(Magma) [IsOdd(n mod 2) select (n-1)*(EulerPhi(n))/2 else n*(EulerPhi(n)): n in [1..52]]; // Vincenzo Librandi, Feb 03 2016

Crossrefs

Cf. A268341.

Sequence in context: A151924 A346205 A343984 * A058524 A072576 A271342

Adjacent sequences: A268339 A268340 A268341 * A268343 A268344 A268345

Keyword

nonn

Author

Michel Marcus, Feb 02 2016

Status

approved