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A144293
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Largest prime factor of n-th Bell number A000110(n) (or 1 if A000110(n) = 1).
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4
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1, 1, 2, 5, 5, 13, 29, 877, 23, 53, 4639, 22619, 2423, 27644437, 1800937, 1101959, 43486067, 255755771, 5006399, 222527, 4326209287, 188633, 574631, 13369534669, 1204457631577, 171659, 11759883224809, 2479031, 171572636187431, 3516743833
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OFFSET
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0,3
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COMMENTS
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The number of refinements of a partition is the product of the Bell numbers of the cell sizes.
The number of encoarsements is the Bell number of the number of cells.
For these to be equal, a Bell number has to be a product of Bell numbers.
This happens if there are n-1 single-element cells and 1 n-element cell.
Does it ever happen otherwise? (End)
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LINKS
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MATHEMATICA
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Join[{1}, Table[FactorInteger[BellB[n]][[-1, 1]], {n, 40}]] (* Vincenzo Librandi, Jan 04 2017 *)
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PROG
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(Magma) [1, 1] cat [Maximum(PrimeDivisors(Bell(n))): n in [2..30]]; // Vincenzo Librandi, Jan 04 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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