A088035 -id:A088035 - cp's OEIS frontend

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

Amarnath Murthy, Sep 19 2003

nonn

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

Cf. A068601, A088035.

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

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

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

Corrected and extended by Ray Chandler, Sep 23 2003

Definition clarified by Harvey P. Dale, Oct 05 2017

A088069 Cubes sandwiched between two numbers divisible by cubes > 1.

Original entry on oeis.org

4913, 6859, 166375, 704969, 2048383, 4173281, 7880599, 12649337, 15438249, 15813251, 19902511, 28372625, 34328125, 40353607, 53582633, 71473375, 90518849, 115501303, 141420761, 174676879, 208527857, 251239591, 294079625

Offset: 1

Amarnath Murthy, Sep 22 2003

nonn

Sequence is infinite. If k is a member then so is k^3. Subsidiary sequence: fourth powers sandwiched between two numbers divisible by fourth powers.

			4913 = 17^3 is a term since 4912 is divisible by 8 and 4914 is divisible by 27.

Subsequence of A088035.

Cf. A088068.

Select[Range[2, 1000], Last[Union[Transpose[FactorInteger[ #^3 - 1]][[2]]]] > 2 && Last[Union[Transpose[FactorInteger[ #^3 + 1]][[2]]]] > 2 &]^3 (* Tanya Khovanova, Sep 08 2007 *)

Corrected and extended by Ray Chandler, Sep 27 2003

Offset changed by Andrew Howroyd, Sep 22 2024

cp's OEIS Frontend

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

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