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A370076
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Numbers k such that A005361(k) is prime.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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... .
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LINKS
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MATHEMATICA
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Select[Range[200], PrimeQ[Times @@ FactorInteger[#][[;; , 2]]] &]
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PROG
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(PARI) is(n) = isprime(vecprod(factor(n)[ , 2]));
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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