A337257 Number of even divisors of n!.

0, 0, 1, 2, 6, 12, 24, 48, 84, 140, 240, 480, 720, 1440, 2376, 3696, 5040, 10080, 13824, 27648, 38880, 57600, 91200, 182400, 232320, 325248, 510048, 649152, 882000, 1764000, 2246400, 4492800, 5356800, 7618560, 11796480, 15925248

Offset: 0

Author

Gus Wiseman, Aug 23 2020

Keywords

• nonn

Examples

			The a(2) = 1 through a(5) = 12 divisors:
  2  2  2   2
     6  4   4
        6   6
        8   8
        12  10
        24  12
            20
            24
            30
            40
            60
            120
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

A336940 is the odd version.

A000265 gives the maximum odd divisor of n.

A001227 counts odd divisors.

A183063 counts even divisors.

Cf. A000005, A001013, A001055, A006939, A049606, A124010, A253249.

Factorial numbers: A000142, A022559, A027423 (divisors), A048656, A071626, A076716 (factorizations), A325272, A325273, A325617, A336414, A336498.

Programs

Mathematica

Table[Length[Select[Divisors[n!],EvenQ]],{n,0,15}]

PARI

a(n) = sumdiv(n!, d, !(d%2)); \\ Michel Marcus, Aug 24 2020

Formula

a(n) = A183063(n!).

A336940(n) + a(n) = A027423(n) = A000005(n!).