A122692 Cubeful numbers whose neighbors are also cubeful.

1376, 4375, 4913, 5751, 6859, 13311, 13376, 16120, 21249, 22625, 22626, 24353, 25624, 28376, 31375, 32751, 33615, 40473, 41743, 48249, 49625, 49735, 52624, 55376, 57968, 58375, 59751, 75249, 76625, 79624, 82376, 85375, 86751, 90208

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..3903 (first 1000 terms from Harvey P. Dale)

Example

1376 is divisible by 8, and its neighbors 1375 and 1377 are divisible by 125 and 27, respectively.

Maple

N := 10^6: # get all terms <= N
CF := {seq(seq(x^3 * y, y = 1..floor(N/x^3)), x = 2..floor(N^(1/3)))}:
CF intersect map(`-`, CF, 1) intersect map(`+`, CF, 1): # Robert Israel, Jul 16 2014

Mathematica

Select[Range[2, 100000], Max[Transpose[FactorInteger[ # ]][[2]]] >= 3 && Max[Transpose[FactorInteger[# + 1]][[2]]] >= 3 && Max[Transpose[FactorInteger[# - 1]][[2]]] >= 3 &]
cnQ[{a_, b_, c_}] := And@@(# > 2 &/@{a, b, c}); Flatten[Position[Partition[Table[Max[Transpose[FactorInteger[n]][[2]]], {n, 91000}], 3, 1], _?(cnQ[#] &)]] + 1 (* Harvey P. Dale, Jul 28 2013 *)

Prog

(PARI)
iscubefree(n) = vecsort(factor(n)~, 2, 4)[2, 1] < 3
s = []; for(n = 3, 200000, if(!iscubefree(n - 1) && !iscubefree(n) && !iscubefree(n + 1), s = concat(s, n))); s \\ Colin Barker, Jul 16 2014
(PARI) A051903(n)=if(n>1, vecmax(factor(n)[, 2]), 0)
is(n)=A051903(n)>2 && A051903(n-1)>2 && A051903(n+1)>2 \\ Charles R Greathouse IV, Jul 23 2014

Crossrefs

Cf. Subsequence of A068140 - Smaller of the two consecutive numbers divisible by a cube.

Sequence in context: A056049 A206340 A056087 * A076760 A283231 A283790

Adjacent sequences: A122689 A122690 A122691 * A122693 A122694 A122695

Keyword

nonn

Author

Tanya Khovanova, Oct 21 2006

Status

approved