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A370076
Numbers k such that A005361(k) is prime.
1
4, 8, 9, 12, 18, 20, 24, 25, 27, 28, 32, 40, 44, 45, 49, 50, 52, 54, 56, 60, 63, 68, 75, 76, 84, 88, 90, 92, 96, 98, 99, 104, 116, 117, 120, 121, 124, 125, 126, 128, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 164, 168, 169, 171, 172, 175, 184, 188
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
MATHEMATICA
Select[Range[200], PrimeQ[Times @@ FactorInteger[#][[;; , 2]]] &]
PROG
(PARI) is(n) = isprime(vecprod(factor(n)[ , 2]));
CROSSREFS
Cf. A005117, A005361, A053810 (subsequence), A059956.
Similar sequences: A009087, A023194.
Sequence in context: A119025 A167903 A074661 * A252849 A375229 A082293
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 08 2024
STATUS
approved