A097380 Numbers m such that 1+CubeFreeKernel(m) is prime.

1, 2, 4, 6, 8, 10, 12, 16, 18, 22, 24, 28, 30, 32, 36, 42, 46, 48, 52, 54, 56, 58, 60, 64, 66, 70, 72, 78, 82, 96, 100, 102, 104, 106, 108, 112, 120, 126, 128, 130, 138, 144, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 200, 208, 210, 216, 222, 224, 226

Offset

1,2

Links

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

Formula

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

Example

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

Mathematica

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A306263 A071596 A090778 * A114270 A109884 A015926

Adjacent sequences: A097377 A097378 A097379 * A097381 A097382 A097383

Keyword

nonn

Author

Reinhard Zumkeller, Aug 11 2004

Status

approved