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%I #27 Sep 27 2024 13:43:19
%S 4,8,9,12,18,20,24,32,36,40,44,45,48,49,50,56,60,63,72,75,80,81,84,88,
%T 90,92,99,104,108,116,117,128,132,136,140,144,147,153,156,160,162,164,
%U 168,169,180,184,200,204,207,212,216,224,225,234,240,243,245,250
%N Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).
%e 12 is a term, because 12 - rad(12) + 1 = 12 - (2*3) + 1 = 12 - 6 + 1 = 7 is prime.
%t rad[n_] := Times @@ (First@# & /@ FactorInteger@ n);Select[Range[250],PrimeQ[#-rad[#]+1]&] (* _James C. McMahon_, Sep 27 2024 *)
%o (PARI) isok(k) = isprime(k - (factorback(factor(k)[, 1])) + 1);
%Y Cf. A007947, A097379, A359213.
%K nonn
%O 1,1
%A _Arsen Vardanyan_, Aug 23 2024