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A229334 Product of numbers of elements of nonempty subsets of divisors of n. 0
1, 2, 2, 24, 2, 20736, 2, 20736, 24, 20736, 2, 11501279977342425366528000000, 2, 20736, 20736, 309586821120, 2, 11501279977342425366528000000, 2, 11501279977342425366528000000, 20736, 20736, 2 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..23.

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

Cf. A000005, A100587, A229333.

Sequence in context: A093355 A122962 A048648 * A120065 A250033 A224479

Adjacent sequences:  A229331 A229332 A229333 * A229335 A229336 A229337

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Sep 30 2013

STATUS

approved

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Last modified April 6 11:38 EDT 2020. Contains 333273 sequences. (Running on oeis4.)