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A229336
Product of sums of elements of nonempty subsets of divisors of n.
3
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).
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 20 2013
STATUS
approved