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A374593 Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).

%I A374593 #32 Jun 27 2025 16:26:44
%S A374593 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 A374593 90,92,99,104,108,116,117,128,132,136,140,144,147,153,156,160,162,164,
%U A374593 168,169,180,184,200,204,207,212,216,224,225,234,240,243,245,250
%N A374593 Numbers k such that k - rad(k) + 1 is prime, where rad(k) is the radical A007947(k).
%C A374593 Includes 4*p for p in A005384, 8*p for p in A007693, and 16*p for p in A228857. - _Robert Israel_, Jun 27 2025
%H A374593 Robert Israel, <a href="/A374593/b374593.txt">Table of n, a(n) for n = 1..10000</a>
%e A374593 12 is a term, because 12 - rad(12) + 1 = 12 - (2*3) + 1 = 12 - 6 + 1 = 7 is prime.
%p A374593 rad:= n -> convert(numtheory:-factorset(n),`*`):
%p A374593 select(k -> isprime(k - rad(k)+1), [$1..1000]); # _Robert Israel_, Jun 27 2025
%t A374593 rad[n_] := Times @@ (First@# & /@ FactorInteger@ n);Select[Range[250],PrimeQ[#-rad[#]+1]&] (* _James C. McMahon_, Sep 27 2024 *)
%o A374593 (PARI) isok(k) = isprime(k - (factorback(factor(k)[, 1])) + 1);
%Y A374593 Cf. A005384, A007693, A007947, A097379, A228857, A359213.
%K A374593 nonn
%O A374593 1,1
%A A374593 _Arsen Vardanyan_, Aug 23 2024