A097379 Numbers m such that 1+SquareFreeKernel(m) is prime.

1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 30, 32, 36, 40, 42, 44, 46, 48, 50, 54, 58, 60, 64, 66, 70, 72, 78, 80, 82, 84, 88, 90, 92, 96, 100, 102, 106, 108, 116, 120, 126, 128, 130, 132, 138, 140, 144, 150, 156, 160, 162, 164, 166, 168, 176, 178, 180, 184, 190, 192

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2004

Keywords

• nonn

Examples

			m = 100 = (2*5)^2 -> A076618(100) = 1+2*5 = 11 = A000040(5), therefore 100 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007947, A076618, A039787, A097380, A097381, A359213.

Programs

Mathematica

Select[Range[200], PrimeQ[1 + Times @@ FactorInteger[#][[;; , 1]]] &] (* Amiram Eldar, Feb 01 2024 *)

PARI

is(n) = isprime(1 + vecprod(factor(n)[, 1])); \\ Amiram Eldar, Feb 01 2024

Formula

A076618(a(n)) = A007947(a(n))+1 is prime.