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Search: id:A067132
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| A067132 |
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Number of elements in the largest set of divisors of n which are in geometric progression. |
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+0
2
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| 1, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 3, 2, 2, 2, 5, 2, 3, 2, 3, 2, 2, 2, 4, 3, 2, 4, 3, 2, 2, 2, 6, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 5, 3, 3, 2, 3, 2, 4, 2, 4, 2, 2, 2, 3, 2, 2, 3, 7, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 3, 3, 2, 2, 2, 5, 5, 2, 2, 3, 2, 2, 2, 4, 2, 3, 2, 3, 2, 2, 2, 6, 2, 3, 3, 3, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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If the prime factorization of n>1 is p_1^e_1 ... p_k^e_k, then a(n) = 1+max(e_1, ...e_k).
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EXAMPLE
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a(12) = 3 as the divisors of 12 are {1,2,3,4,6,12} and the maximal subsets in geometric progression are {1,2,4} and {3,6,12}. a(16) = 5; the maximal set is {1,2,4,8,16}.
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MATHEMATICA
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a[n_] := If[n==1, 1, Max@@Last/@FactorInteger[n]+1]
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CROSSREFS
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Cf. A000961, A067131.
Sequence in context: A082091 A085962 A060244 this_sequence A089132 A107259 A121041
Adjacent sequences: A067129 A067130 A067131 this_sequence A067133 A067134 A067135
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jan 09 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Jan 15 2002
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