A088036 Numbers k such that k^3 - 1 is divisible by a cube other than 1.

9, 10, 17, 18, 19, 25, 28, 33, 37, 41, 46, 49, 55, 57, 64, 65, 73, 81, 82, 89, 91, 97, 100, 105, 109, 113, 118, 121, 126, 127, 129, 136, 137, 145, 153, 154, 161, 163, 169, 172, 177, 181, 185, 190, 193, 199, 201, 208, 209, 217, 225, 226, 233, 235, 241, 244, 249

Offset: 1

Author

Amarnath Murthy, Sep 19 2003

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1185

Crossrefs

Cf. A068601, A088035.

Programs

Maple

isA046099 := proc(n)
    local p;
    for p in ifactors(n)[2] do
        if op(2,p) >= 3 then
            return true;
        end if;
    end do:
    false ;
end proc:
n := 1;
for i from 1 to 5000 do
    if isA046099(i^3-1) then
        printf("%d %d\n",n,i) ;
        n := n+1;
    end if;
end do: # R. J. Mathar, Dec 03 2015

Mathematica

n3dcQ[n_]:=Count[Divisors[n^3-1]],?(IntegerQ[Surd[#,3]]&)>1; Select[ Range[ 2,250],n3dcQ] (* _Harvey P. Dale, Oct 05 2017 *)

Python

from sympy import factorint
def ok(n): return max(factorint(n**3 - 1).values()) >= 3
print(list(filter(ok, range(1, 250)))) # Michael S. Branicky, Sep 10 2021

Extensions

Corrected and extended by Ray Chandler, Sep 23 2003

Definition clarified by Harvey P. Dale, Oct 05 2017