

A296522


Number of disjoint covering systems of cardinality n with gcd of the moduli equal to 1.


0



1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,13


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..13.
I. P. Goulden, L. B. Richmond, and J. Shallit, Natural exact covering systems and the reversion of the MÃ¶bius series, arXiv:1711.04109 [math.NT], 2017.


EXAMPLE

An example of one of the 30 DCS with GCD 1 counted by a(13) is as follows:
x == 0,2 (mod 6)
x == 1,3,5,7 (mod 10)
x == 4 (mod 15)
x == 9,10,16,22,28,29 (mod 30)
Note that gcd(6,10,15,30) = 1.


CROSSREFS

Sequence in context: A219015 A144839 A124992 * A023926 A022068 A277043
Adjacent sequences: A296519 A296520 A296521 * A296523 A296524 A296525


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Dec 14 2017


STATUS

approved



