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A212164
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Numbers n such that the maximal exponent in its prime factorization is greater than the number of positive exponents (A051903(n) > A001221(n)).
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11
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4, 8, 9, 16, 24, 25, 27, 32, 40, 48, 49, 54, 56, 64, 72, 80, 81, 88, 96, 104, 108, 112, 121, 125, 128, 135, 136, 144, 152, 160, 162, 169, 176, 184, 189, 192, 200, 208, 216, 224, 232, 240, 243, 248, 250, 256, 272, 288, 289, 296, 297, 304, 320, 324, 328, 336
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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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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].
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EXAMPLE
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40 = 2^3*5^1 has 2 distinct prime factors, hence, 2 positive exponents in its prime factorization (namely, 3 and 1, although the 1 is often left implicit). 2 is less than the maximal exponent in 40's prime factorization, which is 3. Therefore, 40 belongs to the sequence.
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MATHEMATICA
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okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] > Length[f]]; Select[Range[1000], okQ] (* T. D. Noe, May 24 2012 *)
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PROG
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(Haskell)
import Data.List (elemIndices)
a212164 n = a212164_list !! (n-1)
a212164_list = map (+ 1) $ findIndices (< 0) a225230_list
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CROSSREFS
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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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