A229334 - OEIS

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A229334

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

1, 2, 2, 24, 2, 20736, 2, 20736, 24, 20736, 2, 11501279977342425366528000000, 2, 20736, 20736, 309586821120, 2, 11501279977342425366528000000, 2, 11501279977342425366528000000, 20736, 20736, 2

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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