%I #10 Aug 27 2020 00:15:18
%S 0,0,1,2,6,12,24,48,84,140,240,480,720,1440,2376,3696,5040,10080,
%T 13824,27648,38880,57600,91200,182400,232320,325248,510048,649152,
%U 882000,1764000,2246400,4492800,5356800,7618560,11796480,15925248
%N Number of even divisors of n!.
%H Seiichi Manyama, <a href="/A337257/b337257.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A183063(n!).
%F A336940(n) + a(n) = A027423(n) = A000005(n!).
%e The a(2) = 1 through a(5) = 12 divisors:
%e 2 2 2 2
%e 6 4 4
%e 6 6
%e 8 8
%e 12 10
%e 24 12
%e 20
%e 24
%e 30
%e 40
%e 60
%e 120
%t Table[Length[Select[Divisors[n!],EvenQ]],{n,0,15}]
%o (PARI) a(n) = sumdiv(n!, d, !(d%2)); \\ _Michel Marcus_, Aug 24 2020
%Y A336940 is the odd version.
%Y A000265 gives the maximum odd divisor of n.
%Y A001227 counts odd divisors.
%Y A183063 counts even divisors.
%Y Cf. A000005, A001013, A001055, A006939, A049606, A124010, A253249.
%Y Factorial numbers: A000142, A022559, A027423 (divisors), A048656, A071626, A076716 (factorizations), A325272, A325273, A325617, A336414, A336498.
%K nonn
%O 0,4
%A _Gus Wiseman_, Aug 23 2020