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 A303703 #5 May 02 2018 09:22:02 %S A303703 1,2,3,6,8,12,24,30,60,120,144,180,240,360,720,840,1680,2520,5040, %T A303703 5760,6720,10080,20160,40320,45360,60480,90720,120960,181440,362880, %U A303703 403200,453600,725760,907200,1209600,1814400,3628800,3991680 %N A303703 Positive numbers that are congruent mod k! to a divisor of k! for any k > 0. %C A303703 This sequence is infinite as it contains all factorial numbers (A000142). %H A303703 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a> %e A303703 8 == 1 mod 1! and 1 divides 1!, 8 == 2 mod 2! and 2 divides 2!, 8 == 2 mod 3! and 2 divides 3!, 8 divides k! for any k > 3, hence 8 appears in the sequence. %e A303703 42 == 18 mod 4! and 18 is not a divisor of 4!, hence 42 does not appear in the sequence. %o A303703 (PARI) is(n) = my (f=1); for (k=1, oo, f*=k; if (f%n==0, return (1), (n%f) && (f%(n%f)), return (0))) %Y A303703 Cf. A000142. %K A303703 nonn %O A303703 1,2 %A A303703 _Rémy Sigrist_, Apr 29 2018