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A122692 Cubeful numbers such that their neighbors are also cubeful. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

EXAMPLE

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

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

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Last modified March 27 08:56 EDT 2017. Contains 284146 sequences.