A229334 - OEIS

%I #7 Dec 11 2015 22:04:33

%S 1,2,2,24,2,20736,2,20736,24,20736,2,11501279977342425366528000000,2,

%T 20736,20736,309586821120,2,11501279977342425366528000000,2,

%U 11501279977342425366528000000,20736,20736,2

%N Product of numbers of elements of nonempty subsets of divisors of n.

%C Number of nonempty subsets of divisors of n = A100587(n).

%C Also product of sizes of all the subsets of set of divisors of n.

%F a(n) = product[k=1..tau(n)] k^C(tau(n),k) = product[k=1..tau(n)] k^(tau(n)!/((tau(n)-k)!*k!)).

%e For n = 4; divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; product of numbers of elements of subsets = 1*1*1*2*2*2*3 = 24.

%e For n = 4; tau(4) = 3; a(4) = [1^(3!/((3-1)!*1!))] * [2^(3!/((3-2)!*2!))] * [3^(3!/((3-3)!*3!))] = 1^3 * 2^3 * 3^1 = 24.

%t Table[Times @@ Rest[Length /@ Subsets[Divisors[n]]], {n, 23}] (* _T. D. Noe_, Oct 01 2013 *)

%Y Cf. A000005, A100587, A229333.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 30 2013