This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160560 #32 Aug 04 2025 10:30:04 %S A160560 2,4,6,8,16,18,30,32,40,54,64,126,128,150,162,200,224,256,486,512,750, %T A160560 882,1000,1024,1458,1568,1638,1782,1950,2048,2600,2912,3750,4096,4374, %U A160560 5000,5632,6174,6318,8192,10976 %N A160560 Almost covering numbers. %C A160560 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. %C A160560 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. %C A160560 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 %H A160560 Donald Jason Gibson, <a href="https://doi.org/10.1090/S0025-5718-08-02154-6">A covering system with least modulus 25</a>, Math. Comp. 78, (2009), 1127-1146. %H A160560 Nathan McNew and Jai Setty, <a href="https://arxiv.org/abs/2507.23041">On the densities of covering numbers and abundant numbers</a>, arXiv:2507.23041 [math.NT], 2025. See p. 7. %H A160560 Pace P. Nielsen, <a href="https://doi.org/10.1016/j.jnt.2008.09.016">A covering system whose smallest modulus is 40</a>, Journal of Number Theory 129, (2009), 640-666. %H A160560 Pace P. Nielsen, <a href="http://www.youtube.com/watch?v=3ev1YjVl0RY">A movie explaining covering systems</a>. %e A160560 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. %Y A160560 Cf. A160559. %K A160560 nonn,more %O A160560 1,1 %A A160560 _Matthijs Coster_, May 19 2009 %E A160560 Corrected by _Eric Rowland_, Oct 24 2018 %E A160560 Edited, missing term a(27)=1638 inserted, and a(38)-a(41) added by _Max Alekseyev_, Feb 08 2025