A097381 Numbers m such that 1+SquareFreeKernel(m)*CubeFreeKernel(m) is prime.

1, 2, 6, 10, 12, 14, 18, 24, 26, 48, 54, 60, 66, 74, 84, 94, 96, 98, 110, 120, 130, 132, 134, 146, 162, 168, 170, 192, 204, 206, 210, 230, 234, 240, 264, 300, 314, 326, 336, 372, 384, 386, 406, 408, 430, 466, 470, 474, 480, 486, 490, 528, 570, 588, 600, 634, 646

Offset: 1

Author

Reinhard Zumkeller, Aug 11 2004

Keywords

• nonn

Links

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

Crossrefs

Cf. A007947, A007948, A097379, A097380.

Programs

Mathematica

f[p_, e_] := p^(1 + Min[e, 2]); s[1] = 2; s[n_] := 1 + Times @@ f @@@ FactorInteger[n]; Select[Range[650], PrimeQ[s[#]] &] (* Amiram Eldar, Feb 01 2024 *)

PARI

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

Formula

A097378(a(n)) is prime.