A078779 - OEIS

%I #29 Nov 05 2017 12:43:07

%S 1,2,3,4,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,26,28,29,30,31,33,

%T 34,35,37,38,39,41,42,43,44,46,47,51,52,53,55,57,58,59,60,61,62,65,66,

%U 67,68,69,70,71,73,74,76,77,78,79,82,83,84,85,86,87,89,91,92,93,94,95,97,101

%N Union of S, 2S and 4S, where S = odd squarefree numbers (A056911).

%C Numbers n such that the cyclic group Z_n is a DCI-group.

%C Numbers n such that A008475(n) = A001414(n).

%C A193551(a(n)) = A000026(a(n)) = a(n). - _Reinhard Zumkeller_, Aug 27 2011

%C Union of squarefree numbers and twice the squarefree numbers (A005117). - _Reinhard Zumkeller_, Feb 11 2012

%C The complement is A046790. - _Omar E. Pol_, Jun 11 2016

%H T. D. Noe, <a href="/A078779/b078779.txt">Table of n, a(n) for n = 1..7098</a>

%H B. Alspach and M. Mishna, <a href="http://dx.doi.org/10.1016/S0012-365X(02)00319-9">Enumeration of Cayley graphs and digraphs</a>, Discr. Math., 256 (2002), 527-539.

%H M. Mishna, <a href="http://people.math.sfu.ca/~mmishna/">Home Page</a>

%H M. Muzychuk, <a href="http://dx.doi.org/10.1016/S0012-365X(97)81804-3">On Adam's conjecture for circulant graphs</a>, Discr. Math. 167 (1997), 497-510.

%F a(n) = (Pi^2/7)*n + O(sqrt(n)). - _Vladimir Shevelev_, Jun 08 2016

%o (Haskell)

%o a078779 n = a078779_list !! (n-1)

%o a078779_list = m a005117_list $ map (* 2) a005117_list where

%o    m xs'@(x:xs) ys'@(y:ys) | x < y     = x : m xs ys'

%o                            | x == y    = x : m xs ys

%o                            | otherwise = y : m xs' ys

%o -- _Reinhard Zumkeller_, Feb 11 2012, Aug 27 2011

%o (PARI) is(n)=issquarefree(n/gcd(n,2)) \\ _Charles R Greathouse IV_, Nov 05 2017

%Y Cf. A121176, A121684, A008475, A001414, A046790.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jan 11 2003

%E Edited by _N. J. A. Sloane_, Sep 13 2006