cp's OEIS Frontend

A337257 Number of even divisors of n!.

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