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A212166
Numbers k such that the maximum exponent in its prime factorization equals the number of positive exponents (A051903(k) = A001221(k)).
9
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
OFFSET
1,2
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)) = 1. - Reinhard Zumkeller, May 03 2013
EXAMPLE
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.
MATHEMATICA
okQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Max[f] == Length[f]]; Select[Range[424], okQ] (* T. D. Noe, May 24 2012 *)
PROG
(Haskell)
import Data.List (elemIndices)
a212166 n = a212166_list !! (n-1)
a212166_list = map (+ 1) $ elemIndices 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
Includes subsequences A000040, A006939, A138534, A181555, A181825.
Cf. A001221, A050326, A051903, A188654 (complement), A225230.
Sequence in context: A119251 A182358 A336418 * A293511 A336615 A325337
KEYWORD
nonn,easy
AUTHOR
Matthew Vandermast, May 22 2012
STATUS
approved