A374593 Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).
4, 8, 9, 12, 18, 20, 24, 32, 36, 40, 44, 45, 48, 49, 50, 56, 60, 63, 72, 75, 80, 81, 84, 88, 90, 92, 99, 104, 108, 116, 117, 128, 132, 136, 140, 144, 147, 153, 156, 160, 162, 164, 168, 169, 180, 184, 200, 204, 207, 212, 216, 224, 225, 234, 240, 243, 245, 250
Offset: 1
Keywords
Examples
12 is a term, because 12 - rad(12) + 1 = 12 - (2*3) + 1 = 12 - 6 + 1 = 7 is prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
rad:= n -> convert(numtheory:-factorset(n),`*`): select(k -> isprime(k - rad(k)+1), [$1..1000]); # Robert Israel, Jun 27 2025
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Mathematica
rad[n_] := Times @@ (First@# & /@ FactorInteger@ n);Select[Range[250],PrimeQ[#-rad[#]+1]&] (* James C. McMahon, Sep 27 2024 *)
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PARI
isok(k) = isprime(k - (factorback(factor(k)[, 1])) + 1);
Comments