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A229336
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Product of sums of elements of nonempty subsets of divisors of n.
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3
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1, 6, 12, 5040, 30, 77598259200, 56, 1307674368000, 168480, 12703122432000, 132, 52875224823823084892891318660312910903645116196873830400000000000000, 182, 440505199411200, 493242753024000, 8222838654177922817725562880000000, 306
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OFFSET
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1,2
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COMMENTS
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Number of nonempty subsets of divisors of n = A100587(n).
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LINKS
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FORMULA
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a(2^n) = (2^(n+1) - 1)!.
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EXAMPLE
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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!.
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MATHEMATICA
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Table[Times@@(Total/@Rest[Subsets[Divisors[n]]]), {n, 20}] (* Harvey P. Dale, Jan 22 2023 *)
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CROSSREFS
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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).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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