cp's OEIS Frontend

A081256 Greatest prime factor of n^3 + 1.

%I A081256 #32 Oct 25 2024 09:31:08
%S A081256 2,3,7,13,7,31,43,19,73,13,37,19,157,61,211,241,13,307,7,127,421,463,
%T A081256 13,79,601,31,37,757,271,67,19,331,151,1123,397,97,43,67,1483,223,547,
%U A081256 1723,139,631,283,109,103,61,181,43,2551,379,919,409,2971,79,103,3307,163
%N A081256 Greatest prime factor of n^3 + 1.
%C A081256 Record values appear to match the terms of A002383 for n>1. - _Bill McEachen_, Oct 18 2023
%H A081256 R. J. Mathar and T. D. Noe, <a href="/A081256/b081256.txt">Table of n, a(n) for n = 1..10000</a> (first 5000 terms from R. J. Mathar)
%H A081256 J. Buchmann, K. Győry, M. Mignotte, and N. Tzanakis, <a href="https://doi.org/10.5486/PMD.1991.38.1-2.15">Lower bounds for P(x^3+k), an elementary approach</a>, Publ. Math. Debrecen, Vol. 38, No. 1-2 (1991), pp. 145-163.
%F A081256 a(n) = A006530(A001093(n)). - _M. F. Hasler_, Jun 13 2018
%F A081256 a(n) >= 31 for n >= 70 (Buchmann et al., 1991). - _Amiram Eldar_, Oct 25 2024
%p A081256 A081256 := proc(n)
%p A081256     A006530(n^3+1) ;
%p A081256 end proc:
%p A081256 seq(A081256(n),n=1..20) ; # _R. J. Mathar_, Feb 13 2014
%t A081256 Table[Max[Transpose[FactorInteger[n^3 + 1]][[1]]], {n, 25}]
%o A081256 (PARI) a(n)=my(f=factor(n^3+1)); f[#f~,1] \\ _Charles R Greathouse IV_, Mar 08 2017
%o A081256 (PARI) A081256(n)=vecmax(factor(n^3+1)[,1]) \\ It seems slightly slower to get the last element using ...[-1..-1][1]. - _M. F. Hasler_, Jun 15 2018
%Y A081256 Cf. A081257, A081258, A096173, A096174.
%Y A081256 Cf. A006530, A001093, A002383, A014442, A096172.
%K A081256 easy,nonn
%O A081256 1,1
%A A081256 _Jan Fricke_, Mar 14 2003
%E A081256 More terms from _Harvey P. Dale_, Mar 22 2003
%E A081256 More terms from _Hugo Pfoertner_, Jun 20 2004