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Numbers m such that 1+CubeFreeKernel(m) is prime.
5

%I #12 Feb 01 2024 01:48:40

%S 1,2,4,6,8,10,12,16,18,22,24,28,30,32,36,42,46,48,52,54,56,58,60,64,

%T 66,70,72,78,82,96,100,102,104,106,108,112,120,126,128,130,138,144,

%U 148,150,156,162,166,172,178,180,190,192,196,198,200,208,210,216,222,224,226

%N Numbers m such that 1+CubeFreeKernel(m) is prime.

%H Amiram Eldar, <a href="/A097380/b097380.txt">Table of n, a(n) for n = 1..10000</a>

%F A097377(a(n)) = A007948(a(n))+1 is prime.

%e m = 216 = (2*3)^3 -> A097377(216) = 1+(2*3)^2 = 37 = A000040(12), therefore 216 is a term.

%t f[p_, e_] := p^Min[e, 2]; s[1] = 2; s[n_] := 1 + Times @@ f @@@ FactorInteger[n]; Select[Range[230], PrimeQ[s[#]] &] (* _Amiram Eldar_, Feb 01 2024 *)

%o (PARI) is(n) = {my(f = factor(n)); isprime(1 + prod(i = 1, #f~, f[i, 1]^min(f[i, 2], 2)));} \\ _Amiram Eldar_, Feb 01 2024

%Y Cf. A007948, A089189, A097377, A097379, A097381.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Aug 11 2004