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A212166
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Numbers n such that the maximal exponent in its prime factorization equals the number of positive exponents (A051903(n) = A001221(n)).
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8
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1, 2, 3, 5, 7, 11, 12, 13, 17, 18, 19, 20, 23, 28, 29, 31, 36, 37, 41, 43, 44, 45, 47, 50, 52, 53, 59, 61, 63, 67, 68, 71, 73, 75, 76, 79, 83, 89, 92, 97, 98, 99, 100, 101, 103, 107, 109, 113, 116, 117, 120, 124, 127, 131, 137, 139, 147, 148, 149, 151, 153
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OFFSET
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1,2
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COMMENTS
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A225230(a(n)) = 0; A050326(a(n)) = 1. - Reinhard Zumkeller, May 03 2013
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Primefan, The First 2500 Integers Factored (first of 5 pages)
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EXAMPLE
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36 = 2^2*3^2 has 2 positive exponents in its prime factorization. The maximal exponent in its prime factorization is also 2. Therefore, 36 belongs to this sequence.
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MATHEMATICA
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okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] == Length[f]]; Select[Range[424], okQ] (* T. D. Noe, May 24 2012 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a212166 n = a212166_list !! (n-1)
a212166_list = map (+ 1) $ elemIndices 0 a225230_list
-- Reinhard Zumkeller, May 03 2013
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CROSSREFS
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Includes subsequences A000040, A006939, A138534, A181555, A181825. See also A212164-A212165, A212167-A212168.
Cf. A188654 (complement).
Sequence in context: A073085 A119251 A182358 * A212127 A028835 A028834
Adjacent sequences: A212163 A212164 A212165 * A212167 A212168 A212169
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KEYWORD
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nonn
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AUTHOR
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Matthew Vandermast, May 22 2012
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STATUS
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approved
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