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