A229336 Product of sums of elements of nonempty subsets of divisors of n.

1, 6, 12, 5040, 30, 77598259200, 56, 1307674368000, 168480, 12703122432000, 132, 52875224823823084892891318660312910903645116196873830400000000000000, 182, 440505199411200, 493242753024000, 8222838654177922817725562880000000, 306

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..17.

Formula

a(2^n) = (2^(n+1) - 1)!.

Example

For n = 2^2 = 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 sums of elements of subsets = 1*2*4*3*5*6*7 = 5040 = (2^3 - 1)! = 7!.

Mathematica

Table[Times@@(Total/@Rest[Subsets[Divisors[n]]]), {n, 20}] (* Harvey P. Dale, Jan 22 2023 *)

Crossrefs

Cf. A229335 (sum of sums of elements of nonempty subsets of divisors of n),

A229337 (sum of products of elements of nonempty subsets of divisors of n),

A229338 (product of products of elements of nonempty subsets of divisors of n).

Sequence in context: A159282 A202383 A216423 * A363755 A070396 A359091

Adjacent sequences: A229333 A229334 A229335 * A229337 A229338 A229339

Keyword

nonn

Author

Jaroslav Krizek, Sep 20 2013

Status

approved