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A212164
Numbers k such that the maximum exponent in its prime factorization is greater than the number of positive exponents (A051903(k) > A001221(k)).
11
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
OFFSET
1,1
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
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).
FORMULA
A225230(a(n)) < 0; A050326(a(n)) = 0. - Reinhard Zumkeller, May 03 2013
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 !! (n-1)
a212164_list = map (+ 1) $ findIndices (< 0) a225230_list
-- Reinhard Zumkeller, May 03 2013
(PARI) is(k) = {my(e = factor(k)[, 2]); #e && vecmax(e) > #e; } \\ Amiram Eldar, Sep 08 2024
CROSSREFS
Complement of A212167.
See also A212165, A212166, A212168.
Subsequence of A188654.
Sequence in context: A372280 A361204 A245080 * A293243 A339740 A345171
KEYWORD
nonn,easy
AUTHOR
Matthew Vandermast, May 22 2012
STATUS
approved