OFFSET
1,2
COMMENTS
Jakimczuk (2024) proved:
The number of terms that do not exceed x is N(x) = c * x^(1/3) / 2 + o(x^(1/3)) where c = A362974.
The relative asymptotic density of this sequence within the cubefull numbers is 1/2.
In general, the relative asymptotic density of the s-full numbers (numbers whose exponents in their prime factorization are all >= s) with an even number of prime factors (counted with multiplicity) within the s-full numbers is 1/2 when s is odd.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Rafael Jakimczuk, Arithmetical Functions over the Powerful Part of an Integer, ResearchGate, 2024.
MATHEMATICA
q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, # > 2 &] && OddQ[Total[e]]]; Select[Range[30000], q]
PROG
(PARI) is(n) = {my(e = factor(n)[, 2]); n > 1 && vecmin(e) > 2 && vecsum(e)%2; }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 02 2024
STATUS
approved