A081258 Numbers k > 1 such that k^3 - 1 (or equivalently k^2 + k + 1) has no prime factor greater than k.

16, 18, 22, 30, 49, 67, 68, 74, 79, 81, 87, 100, 102, 121, 135, 137, 146, 149, 154, 158, 159, 163, 165, 169, 172, 178, 181, 191, 211, 221, 229, 230, 235, 256, 262, 263, 269, 273, 277, 291, 292, 301, 305, 313, 315, 324, 326, 334, 352, 361, 372, 373, 380, 393

Offset: 1

Author

Jan Fricke, Mar 14 2003

Keywords

• easy
• nonn

Comments

One might also include 1 as a term here. - R. J. Mathar, Oct 11 2011

Examples

			16 is a term: 16^3 - 1 = 4095 = 3*3*5*7*13.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A081256, A081257.

Programs

Maple

isA081258 := proc(n)
        numtheory[factorset](n^3-1) ;
        if max(op(%)) <= n then
                true;
        else
                false;
        end if;
end proc;
for n from 1 to 400 do
        if isA081258(n) then
                printf("%d,",n);
        end if;
end do: # R. J. Mathar, Oct 11 2011

Mathematica

Select[Range[2, 1000], FactorInteger[#^3 - 1][[-1, 1]] <= #&] (* Jean-François Alcover, Jun 15 2020 *)

Extensions

Name changed by Robert Israel, Nov 11 2016