A383220 Integers k such that rad(k)*2^(k/rad(k)) + 1 is prime where rad = A007947.

1, 2, 3, 5, 6, 11, 14, 15, 20, 21, 23, 24, 26, 29, 30, 33, 35, 39, 41, 44, 51, 53, 65, 68, 69, 74, 78, 83, 86, 88, 89, 90, 95, 105, 111, 113, 114, 116, 117, 119, 125, 126, 131, 134, 135, 138, 140, 141, 146, 147, 153, 155, 156, 158, 165, 168, 171, 173, 174, 179

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 19 2025

Keywords

• nonn

Examples

			20 is a term because 10*2^(20/10) + 1 = 41 is prime, where 10 is largest squarefree divisor of k = 20.
		

Crossrefs

Supersequence of A005384.

Cf. A002234, A003557, A007947.

Programs

Magma

[k: k in [1..180] | IsPrime(&*PrimeDivisors(k)*2^(k div &*PrimeDivisors(k))+1)];

Mathematica

s={};Do[r=Last[Select[Divisors[n], SquareFreeQ]];If[PrimeQ[r*2^(n/r)+1],AppendTo[s,n]],{n,179}];s (* James C. McMahon, May 01 2025~ *)

PARI

isok(k) = my(r=factorback(factorint(k)[, 1])); ispseudoprime(r*2^(k/r) + 1); \\ Michel Marcus, Apr 20 2025