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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A068601, A088035.

Sequence in context: A173015 A045568 A191380 * A217935 A100595 A107433

Adjacent sequences: A088033 A088034 A088035 * A088037 A088038 A088039

Keyword

nonn

Author

Amarnath Murthy, Sep 19 2003

Extensions

Corrected and extended by Ray Chandler, Sep 23 2003

Definition clarified by Harvey P. Dale, Oct 05 2017

Status

approved