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A374593
Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).
1
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
1,1
EXAMPLE
12 is a term, because 12 - rad(12) + 1 = 12 - (2*3) + 1 = 12 - 6 + 1 = 7 is prime.
MATHEMATICA
rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); Select[Range[250], PrimeQ[#-rad[#]+1]&] (* James C. McMahon, Sep 27 2024 *)
PROG
(PARI) isok(k) = isprime(k - (factorback(factor(k)[, 1])) + 1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Arsen Vardanyan, Aug 23 2024
STATUS
approved