OFFSET
1,1
COMMENTS
Cubeful numbers with cubeful successors. This is to cubes as A068781 is to squares. 1375 is the smallest of three consecutive numbers divisible by a cube, since 1375 = 5^3 * 11 and 1376 = 2^5 * 43 and 1377 = 3^4 * 17. What is the smallest of four consecutive numbers divisible by a cube? Of n consecutive numbers divisible by a cube? - Jonathan Vos Post, Sep 18 2007
22624 is the smallest of four consecutive numbers each divisible by a cube, with factorizations 2^5 * 7 * 101, 5^3 * 181, 2 * 3^3 * 419, and 11^3 * 17. - D. S. McNeil, Dec 10 2010
18035622 is the smallest of five consecutive numbers each divisible by a cube. 4379776620 is the smallest of six consecutive numbers each divisible by a cube. 1204244328624 is the smallest of seven consecutive numbers each divisible by a cube. - Donovan Johnson, Dec 13 2010
The sequence is the union, over all pairs of distinct primes (p,q), of numbers == 0 mod p^3 and == -1 mod q^3 or vice versa. - Robert Israel, Aug 13 2018
The asymptotic density of this sequence is 1 - 2/zeta(3) + Product_{p prime} (1 - 2/p^3) = 1 - 2 * A088453 + A340153 = 0.013077991848467056243... - Amiram Eldar, Feb 16 2021
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
343 is a term as 343 = 7^3 and 344= 2^3 * 43.
MAPLE
isA068140 := proc(n)
isA046099(n) and isA046099(n+1) ;
end proc:
for n from 1 to 4000 do
if isA068140(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Dec 08 2015
MATHEMATICA
a = b = 0; Do[b = Max[ Transpose[ FactorInteger[n]] [[2]]]; If[a > 2 && b > 2, Print[n - 1]]; a = b, {n, 2, 5000}]
Select[Range[2, 6000], Max[Transpose[FactorInteger[ # ]][[2]]] > 2 && Max[Transpose[FactorInteger[ # + 1]][[2]]] > 2 &] (* Jonathan Vos Post, Sep 18 2007 *)
SequencePosition[Table[If[AnyTrue[Rest[Divisors[n]], IntegerQ[Surd[#, 3]]&], 1, 0], {n, 3600}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 18 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Feb 22 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Mar 02 2002
Title edited, cross-references added by Matthew Vandermast, Dec 09 2010
Definition clarified by Harvey P. Dale, Apr 18 2020
STATUS
approved