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A097380
Numbers m such that 1+CubeFreeKernel(m) is prime.
5
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 11 2004
STATUS
approved