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A088036
Numbers k such that k^3 - 1 is divisible by a cube other than 1.
2
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
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
Sequence in context: A173015 A045568 A191380 * A217935 A100595 A107433
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