OFFSET
1,2
COMMENTS
Number of nonempty subsets of divisors of n = A100587(n).
Also product of sizes of all the subsets of set of divisors of n.
FORMULA
a(n) = product[k=1..tau(n)] k^C(tau(n),k) = product[k=1..tau(n)] k^(tau(n)!/((tau(n)-k)!*k!)).
EXAMPLE
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.
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.
MATHEMATICA
Table[Times @@ Rest[Length /@ Subsets[Divisors[n]]], {n, 23}] (* T. D. Noe, Oct 01 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 30 2013
STATUS
approved