

A212164


Numbers n such that the maximal exponent in its prime factorization is greater than the number of positive exponents (A051903(n) > A001221(n)).


9



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
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OFFSET

1,1


COMMENTS

A225230(a(n)) < 0; A050326(a(n)) = 0.  Reinhard Zumkeller, May 03 2013


REFERENCES

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.


LINKS

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)


EXAMPLE

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.


MATHEMATICA

okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] > Length[f]]; Select[Range[1000], okQ] (* T. D. Noe, May 24 2012 *)


PROG

(Haskell)
import Data.List (elemIndices)
a212164 n = a212164_list !! (n1)
a212164_list = map (+ 1) $ findIndices (< 0) a225230_list
 Reinhard Zumkeller, May 03 2013


CROSSREFS

Complement of A212167. See also A212165, A212166, A212168.
Cf. Subsequence of A188654.
Sequence in context: A243180 A100657 A245080 * A293243 A140104 A127398
Adjacent sequences: A212161 A212162 A212163 * A212165 A212166 A212167


KEYWORD

nonn


AUTHOR

Matthew Vandermast, May 22 2012


STATUS

approved



