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

2,1

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.

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).

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A006530, A023503, A023509, A087713.

Each term > 4 is element of A006881.

Cf. A000215, A000668, A058383, A268640.

Sequence in context: A272771 A346675 A077038 * A053320 A351649 A019090

Adjacent sequences: A379442 A379443 A379444 * A379446 A379447 A379448

Keyword

nonn

Author

Hugo Pfoertner, Dec 28 2024

Status

approved