A081256 - OEIS

%I #32 Oct 25 2024 09:31:08

%S 2,3,7,13,7,31,43,19,73,13,37,19,157,61,211,241,13,307,7,127,421,463,

%T 13,79,601,31,37,757,271,67,19,331,151,1123,397,97,43,67,1483,223,547,

%U 1723,139,631,283,109,103,61,181,43,2551,379,919,409,2971,79,103,3307,163

%N Greatest prime factor of n^3 + 1.

%C Record values appear to match the terms of A002383 for n>1. - _Bill McEachen_, Oct 18 2023

%H 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 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 a(n) = A006530(A001093(n)). - _M. F. Hasler_, Jun 13 2018

%F a(n) >= 31 for n >= 70 (Buchmann et al., 1991). - _Amiram Eldar_, Oct 25 2024

%p A081256 := proc(n)

%p     A006530(n^3+1) ;

%p end proc:

%p seq(A081256(n),n=1..20) ; # _R. J. Mathar_, Feb 13 2014

%t Table[Max[Transpose[FactorInteger[n^3 + 1]][[1]]], {n, 25}]

%o (PARI) a(n)=my(f=factor(n^3+1)); f[#f~,1] \\ _Charles R Greathouse IV_, Mar 08 2017

%o (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 Cf. A081257, A081258, A096173, A096174.

%Y Cf. A006530, A001093, A002383, A014442, A096172.

%K easy,nonn,changed

%O 1,1

%A _Jan Fricke_, Mar 14 2003

%E More terms from _Harvey P. Dale_, Mar 22 2003

%E More terms from _Hugo Pfoertner_, Jun 20 2004