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 A062309 #20 Jul 17 2024 08:48:31
%S A062309 0,0,2,3,6,50,307,2329,19907,181263,1736542,19044663,220730823,
%T A062309 2845615949,39412442640
%N A062309 Number of ways writing n! as sums of a prime and a nonprime.
%F A062309 a(n) = A062602(n!).
%F A062309 a(n) = n!/2 - A062310(n) - A062311(n) for n >= 2. - _Amiram Eldar_, Jul 17 2024
%e A062309 For n = 4: 4! = 24 = 23+1 = 2+22 = 3+21, so a(4) = 3.
%o A062309 (PARI) a(n) = {my(c = 0, m = n!); forprime(p = 2, m-1, if(!isprime(m - p), c++)); c;} \\ _Amiram Eldar_, Jul 17 2024
%Y A062309 Cf. A000142, A062310, A062311, A062602.
%K A062309 nonn,more
%O A062309 1,3
%A A062309 _Labos Elemer_, Jul 05 2001
%E A062309 a(9)-a(13) from _Sean A. Irvine_, Mar 26 2023
%E A062309 a(14)-a(15) from _Amiram Eldar_, Jul 17 2024