A212166 Numbers k such that the maximum exponent in its prime factorization equals the number of positive exponents (A051903(k) = A001221(k)).

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

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).

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.

See also A212164, A212165, A212167, A212168.

Cf. A001221, A050326, A051903, A188654 (complement), A225230.

Sequence in context: A119251 A182358 A336418 * A293511 A336615 A325337

Adjacent sequences: A212163 A212164 A212165 * A212167 A212168 A212169

Keyword

nonn,easy

Author

Matthew Vandermast, May 22 2012

Status

approved