A081256 Greatest prime factor of n^3 + 1.

2, 3, 7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 13, 307, 7, 127, 421, 463, 13, 79, 601, 31, 37, 757, 271, 67, 19, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 43, 2551, 379, 919, 409, 2971, 79, 103, 3307, 163

Offset: 1

Author

Jan Fricke, Mar 14 2003

Keywords

• easy
• nonn

Comments

Record values appear to match the terms of A002383 for n>1. - Bill McEachen, Oct 18 2023

Links

• R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..10000 (first 5000 terms from R. J. Mathar)
• J. Buchmann, K. Győry, M. Mignotte, and N. Tzanakis, Lower bounds for P(x^3+k), an elementary approach, Publ. Math. Debrecen, Vol. 38, No. 1-2 (1991), pp. 145-163.

Crossrefs

Cf. A081257, A081258, A096173, A096174.

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

Programs

Maple

A081256 := proc(n)
    A006530(n^3+1) ;
end proc:
seq(A081256(n),n=1..20) ; # R. J. Mathar, Feb 13 2014

Mathematica

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

PARI

a(n)=my(f=factor(n^3+1)); f[#f~,1] \\ Charles R Greathouse IV, Mar 08 2017

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

Formula

a(n) = A006530(A001093(n)). - M. F. Hasler, Jun 13 2018

a(n) >= 31 for n >= 70 (Buchmann et al., 1991). - Amiram Eldar, Oct 25 2024

Extensions

More terms from Harvey P. Dale, Mar 22 2003

More terms from Hugo Pfoertner, Jun 20 2004