A075430 Primes with a squarefree neighbor.

2, 3, 5, 7, 11, 13, 23, 29, 31, 37, 41, 43, 47, 59, 61, 67, 71, 73, 79, 83, 101, 103, 107, 109, 113, 131, 137, 139, 157, 167, 173, 179, 181, 191, 193, 211, 223, 227, 229, 239, 257, 263, 277, 281, 283, 311, 313, 317, 331, 347, 353, 359, 367, 373, 383, 389, 397

Offset: 1

Author

Reinhard Zumkeller, Sep 15 2002

Keywords

• nonn

Examples

			a(3) = 5 because 6 (the number above) is squarefree.
a(13) = 47 because 46 (the number below) is squarefree.
53 is not in the sequence because both 52 and 54 have squares among their divisors.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Enrique Pérez Herrero)

Crossrefs

Union of A039787 and A049097.

Complement of A075432 in A000040.

Cf. A005117.

Programs

Mathematica

Select[Prime[Range[100]], Or @@ SquareFreeQ /@ (# + {-1, 1}) &] (* Amiram Eldar, May 07 2025 *)

PARI

isok(p) = isprime(p) && (issquarefree(p-1) || issquarefree(p+1)); \\ Michel Marcus, Feb 20 2023

Sage

def is_A075430(n): return is_prime(n) and (is_squarefree(n-1) or is_squarefree(n+1)) # D. S. McNeil, Jan 16 2011