

A268341


Triangle T(n,k) = Degree of vertex k in the unitary addition Cayley graph Gn, 0<=k<=n1, with T(1,0)=0.


1



0, 1, 1, 2, 1, 1, 2, 2, 2, 2, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 6, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 6, 5, 5, 6, 5, 5, 6, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 10, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
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OFFSET

1,4


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..91.
M. Deaconescu, Adding units mod n, Elem. Math. 55 (2000) 123127.
J. W. Sander, On the addition of units and nonunits mod m, Journal of Number Theory, Volume 129, Issue 10, October 2009, Pages 22602266.
Deepa Sinha, Pravin Garg and Anjali Singh, Some properties of unitary addition Cayley graphs, Notes on Number Theory and Discrete Mathematics, Volume 17, 2011, Number 3, Pages 49—59. See Figure 1 p. 3.


FORMULA

T(n,k) = phi(n) if n is even or if n id odd and gcd(n,k) != 1, phi(n1) if n is odd and gcd(n,k) = 1, where phi is the Euler totient function.


EXAMPLE

Array starts:
0;
1, 1;
2, 1, 1;
2, 2, 2, 2;
4, 3, 3, 3, 3;
2, 2, 2, 2, 2, 2;
6, 5, 5, 5, 5, 5, 5;
...


MATHEMATICA

Table[Which[EvenQ@ n, EulerPhi@ n, OddQ@ n && ! CoprimeQ[n, k], EulerPhi@ n, OddQ@ n && CoprimeQ[n, k], EulerPhi[n]  1], {n, 13}, {k, 0, n  1}] // Flatten (* Michael De Vlieger, Feb 02 2016 *)


PROG

(PARI) T(n, k) = if (n % 2, if (gcd(n, k)==1, eulerphi(n)1, eulerphi(n)), eulerphi(n));


CROSSREFS

Sequence in context: A029285 A134337 A261733 * A053633 A216460 A156755
Adjacent sequences: A268338 A268339 A268340 * A268342 A268343 A268344


KEYWORD

nonn,tabl


AUTHOR

Michel Marcus, Feb 02 2016


STATUS

approved



