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%I #16 Apr 21 2018 06:37:55
%S 1,0,0,0,0,0,0,0,0,0,0,0,30
%N Number of disjoint covering systems of cardinality n with gcd of the moduli equal to 1.
%C A disjoint covering system (DCS) is a system of congruences of the form x == a_i (mod m_i) such that every integer lies in exactly one of the congruences. Here the "moduli" are the m_i.
%H I. P. Goulden, L. B. Richmond, and J. Shallit, <a href="https://arxiv.org/abs/1711.04109">Natural exact covering systems and the reversion of the Möbius series</a>, arXiv:1711.04109 [math.NT], 2017.
%e An example of one of the 30 DCS with GCD 1 counted by a(13) is as follows:
%e x == 0,2 (mod 6)
%e x == 1,3,5,7 (mod 10)
%e x == 4 (mod 15)
%e x == 9,10,16,22,28,29 (mod 30)
%e Note that gcd(6,10,15,30) = 1.
%K nonn,more
%O 1,13
%A _Jeffrey Shallit_, Dec 14 2017
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