OFFSET
1,1
COMMENTS
Numbers of the form m * p^q, where p and q are primes, m is squarefree, and gcd(p, m) = 1.
The asymptotic density of this sequence is (6/Pi^2) * Sum_{p prime} ((p/(p+1)) * Sum_{q prime} 1/p^q) = 0.2933105687... .
The numbers k such that A005361(k) = 1 are the squarefree numbers (A005117), whose asymptotic density is 6/Pi^2 (A059956). The complement of the union of this sequence and the squarefree numbers is the sequence of numbers k such that A005361(k) is composite, whose asymptotic density is 0.0987623... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Range[200], PrimeQ[Times @@ FactorInteger[#][[;; , 2]]] &]
PROG
(PARI) is(n) = isprime(vecprod(factor(n)[ , 2]));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 08 2024
STATUS
approved