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

0,4

Links

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

Formula

a(n) = A183063(n!).

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

Example

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

Mathematica

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

Prog

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

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.

Sequence in context: A118224 A227068 A003680 * A051487 A111286 A058295

Adjacent sequences: A337254 A337255 A337256 * A337258 A337259 A337260

Keyword

nonn

Author

Gus Wiseman, Aug 23 2020

Status

approved