A379445 a(n) = gpf(prime(n)-1)*gpf(prime(n)+1), where gpf is A006530.

4, 6, 6, 15, 21, 6, 15, 33, 35, 10, 57, 35, 77, 69, 39, 145, 155, 187, 21, 111, 65, 287, 55, 21, 85, 221, 159, 33, 133, 14, 143, 391, 161, 185, 95, 1027, 123, 581, 1247, 445, 65, 57, 291, 77, 55, 371, 259, 2147, 437, 377, 85, 55, 35, 86, 1441, 335, 85, 3197, 329, 3337

Offset: 2

Author

Hugo Pfoertner, Dec 28 2024

Keywords

• nonn

Comments

Observation: Even terms of A006881 not occurring in this sequence are, e.g., 22, 34, 38, 46, ..., due to the sparseness of Mersenne primes (A000668) and Fermat primes (A000215). Also missing are many multiples of 3, e.g., 3*{31, 67, 79, 83, 101, 103, 113, ...}, as a consequence of the gaps of A058383 and A268640 and the size distribution of prime factors, i.e., the rareness of smooth numbers.

Examples

			a(43390) = 146 because 2^19-1 = A000668(5) is the 43390th prime and the greatest prime factor of 2^19-2 is 73.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 2..10000
• Hugo Pfoertner, 1 million terms of A379445, 7z compressed file (5 MB) (2025).

Crossrefs

Cf. A006530, A023503, A023509, A087713.

Each term > 4 is element of A006881.

Cf. A000215, A000668, A058383, A268640.

Programs

Mathematica

Table[Times @@ Map[FactorInteger[#][[-1, 1]] &, Prime[n] + {-1, 1}], {n, 2, 61}] (* Michael De Vlieger, Jan 20 2025 *)

PARI

a379445(n) = my (p=prime(n), fm=factor(p-1), fp=factor(p+1)); fm[#fm~,1]*fp[#fp~,1]

Formula

a(n) = A023503(n)*A023509(n). - Michel Marcus, Jan 21 2025