A350964 a(n) is the largest prime factor of 2^p - p^2 where p is the n-th prime.

7, 79, 47, 113, 130783, 523927, 1198297, 240641, 641, 575058377, 1519711993, 65929327, 20105355479017, 9007199254738183, 7633399, 33189241, 21081993227096629777, 951850902549409, 4978773308244222679, 501615233613780359, 9671406556917033397642519, 8251206137, 3818597055399121, 13314319257913, 521211122055087383048446607

Offset: 3

Author

N. J. A. Sloane, Mar 02 2022

Keywords

• nonn

Comments

All prime factors of 2^p - p^2 are congruent to 1 or 7 (mod 8). (See A001132.) - Robert G. Wilson v, Mar 14 2022

References

• E.-B. Escott, Note #1642, L'Intermédiaire des Mathématiciens, 8 (1901), page 12.

Links

• Amiram Eldar, Table of n, a(n) for n = 3..95
• Robert G. Wilson v, Factorization of 2^p - p^2 for n = 3..120

Crossrefs

Cf. A001132, A006530, A072180, A098105, A117587.

Programs

Maple

a:= n-> max(numtheory[factorset]((p-> 2^p-p^2)(ithprime(n)))):
seq(a(n), n=3..27);  # Alois P. Heinz, Mar 03 2022

Mathematica

a[n_] := FactorInteger[2^(p = Prime[n]) - p^2][[-1, 1]]; Array[a, 25, 3] (* Amiram Eldar, Mar 03 2022 *)

PARI

a(n) = my(p=prime(n)); vecmax(factor(2^p - p^2)[,1]); \\ Michel Marcus, Mar 03 2022

Formula

a(n) = A006530(A098105(n)). - Amiram Eldar, Mar 03 2022