A160559 -id:A160559 - cp's OEIS frontend

2, 4, 6, 8, 16, 18, 30, 32, 40, 54, 64, 126, 128, 150, 162, 200, 224, 256, 486, 512, 750, 882, 1000, 1024, 1458, 1568, 1638, 1782, 1950, 2048, 2600, 2912, 3750, 4096, 4374, 5000, 5632, 6174, 6318, 8192, 10976

Offset: 1

Matthijs Coster, May 19 2009

A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a covering system. Let N be the lcm of these moduli. If modulo N we cannot cover all residues, but can cover all but one residue, then N is an almost covering number.
We denote by T(N) the number of divisors of N and by R(N) the smallest number of uncovered numbers modulo N. Suppose N = p^k * M, where gcd(p,M)=1, p is prime, R(M) = 1, and T(M) = p-1, then R(N) = 1 as well.
Some further terms that are obtained this way include: 12750, 13122, 16384, 16758, 17000, 18750, 19602, 21294, 25000, 25350, 26624, 29792, 32768, 33800, 37856, 39366, 43218, 61952, 65536, 74358, 76832, 82134, 93750. - Max Alekseyev, Feb 12 2025

			30 is an almost covering number since 1 mod 2; 2 mod 3; 4 mod 5; 4 mod 6; 8 mod 10; 12 mod 15 and 6 mod 30 covers all numbers modulo 30 except 30-folds.

Donald Jason Gibson, A covering system with least modulus 25, Math. Comp. 78, (2009), 1127-1146.
Nathan McNew and Jai Setty, On the densities of covering numbers and abundant numbers, arXiv:2507.23041 [math.NT], 2025. See p. 7.
Pace P. Nielsen, A covering system whose smallest modulus is 40, Journal of Number Theory 129, (2009), 640-666.
Pace P. Nielsen, A movie explaining covering systems.

Cf. A160559.

Corrected by Eric Rowland, Oct 24 2018

Edited, missing term a(27)=1638 inserted, and a(38)-a(41) added by Max Alekseyev, Feb 08 2025

cp's OEIS Frontend

A160560 Almost covering numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions