cp's OEIS Frontend

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

%I A350964 #38 Jul 15 2022 08:06:57
%S A350964 7,79,47,113,130783,523927,1198297,240641,641,575058377,1519711993,
%T A350964 65929327,20105355479017,9007199254738183,7633399,33189241,
%U A350964 21081993227096629777,951850902549409,4978773308244222679,501615233613780359,9671406556917033397642519,8251206137,3818597055399121,13314319257913,521211122055087383048446607
%N A350964 a(n) is the largest prime factor of 2^p - p^2 where p is the n-th prime.
%C A350964 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
%D A350964 E.-B. Escott, Note #1642, L'Intermédiaire des Mathématiciens, 8 (1901), page 12.
%H A350964 Amiram Eldar, <a href="/A350964/b350964.txt">Table of n, a(n) for n = 3..95</a>
%H A350964 Robert G. Wilson v, <a href="/A350964/a350964_2.txt">Factorization of 2^p - p^2 for n = 3..120</a>
%F A350964 a(n) = A006530(A098105(n)). - _Amiram Eldar_, Mar 03 2022
%p A350964 a:= n-> max(numtheory[factorset]((p-> 2^p-p^2)(ithprime(n)))):
%p A350964 seq(a(n), n=3..27);  # _Alois P. Heinz_, Mar 03 2022
%t A350964 a[n_] := FactorInteger[2^(p = Prime[n]) - p^2][[-1, 1]]; Array[a, 25, 3] (* _Amiram Eldar_, Mar 03 2022 *)
%o A350964 (PARI) a(n) = my(p=prime(n)); vecmax(factor(2^p - p^2)[,1]); \\ _Michel Marcus_, Mar 03 2022
%Y A350964 Cf. A001132, A006530, A072180, A098105, A117587.
%K A350964 nonn
%O A350964 3,1
%A A350964 _N. J. A. Sloane_, Mar 02 2022