A296522 Number of disjoint covering systems of cardinality n with gcd of the moduli equal to 1.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30

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 Möbius 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