OFFSET
1,2
COMMENTS
This sequence is a disjoint union of {1}, the even squarefree numbers (A039956), and the subsequences of even k-free numbers that are not (k-1)-free, for k >= 3. These subsequences include, for k = 3, numbers of the form 4*o where o is an odd cubefree number that is not squarefree (i.e., an odd term of A067259).
The asymptotic density of this sequence is Sum_{k>=2} 1/(zeta(k)*2*(2^k-1)) = 0.222707226888193809... .
The asymptotic mean of the exponent of 2 in the prime factorization of the terms of this sequence is Sum_{k>=2} (k-2)/(zeta(k)*2*(2^k-1)) = 0.24575013985660328894... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
q[n_] := 2^(e = IntegerExponent[n, 2]) < n && e == Max[FactorInteger[n/2^e][[;; , 2]]]; q[1] = True; Select[Range[250], q]
PROG
(PARI) is(n) = {my(e = valuation(n, 2), m = n >> e); n == 1 ||(m > 1 && e == vecmax(factor(m)[, 2]))};
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 21 2023
STATUS
approved