A081257 a(n) is the greatest prime factor of (n^3 - 1).

7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 13, 307, 17, 127, 421, 463, 13, 79, 601, 31, 37, 757, 271, 67, 29, 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: 2

Author

Jan Fricke, Mar 14 2003

Keywords

• easy
• nonn

Comments

The record values here (as well as those for A081256) appear to match the terms of A002383 for n > 1. - Bill McEachen, Jun 19 2023

Examples

			a(7)=19 because 7^3 - 1 = 342 = 2*3*3*19.
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 2..10000 (first 999 terms from R. J. Mathar).

Crossrefs

Cf. A081256, A081258, A002383.

Cf. A096175 (n^3-1 is an odd semiprime), A096176 ((n^3-1)/(n-1) is prime).

Programs

Maple

A081257 := proc(n)
        A006530( n^3-1) ;
end proc: # R. J. Mathar, Jul 18 2015

Mathematica

FactorInteger[#][[-1,1]]&/@(Range[2,60]^3-1) (* Harvey P. Dale, Oct 09 2017 *)

PARI

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

Python

from sympy import primefactors
def A081257(n): return max(primefactors(n-1)+primefactors(n*(n+1)+1)) # Chai Wah Wu, Oct 15 2022

Formula

a(n) = A006530(A068601(n)). - Michel Marcus, Jun 19 2023

Extensions

More terms from Hugo Pfoertner, Jun 21 2004