

A068140


Smaller of two consecutive numbers each divisible by a cube greater than one.


14



80, 135, 296, 343, 351, 375, 512, 567, 624, 728, 783, 944, 999, 1160, 1215, 1375, 1376, 1431, 1592, 1624, 1647, 1808, 1863, 2024, 2079, 2240, 2295, 2375, 2400, 2456, 2511, 2624, 2672, 2727, 2888, 2943, 3087, 3104, 3159, 3320, 3375, 3429, 3536, 3591
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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


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

{k such that k is in A046099 and k+1 is in A046099}.  Jonathan Vos Post, Sep 18 2007


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

Cf. A046099, A063528, A068781, A068782, A068783, A068784, A122692, A174113.
Sequence in context: A062376 A223087 A261549 * A224547 A204648 A202447
Adjacent sequences: A068137 A068138 A068139 * A068141 A068142 A068143


KEYWORD

easy,nonn


AUTHOR

Amarnath Murthy, Feb 22 2002


EXTENSIONS

Edited and extended by Robert G. Wilson v, Mar 02 2002
Title edited, crossreferences added by Matthew Vandermast, Dec 09 2010
Definition clarified by Harvey P. Dale, Apr 18 2020


STATUS

approved



