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Number of even divisors of n!.
2

%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