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A068140
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Smaller of two consecutive numbers each divisible by a cube.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 (jvospost3(AT)gmail.com), 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]
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FORMULA
| {k such that k is in A046099 and k+1 is in A046099}. - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 18 2007
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EXAMPLE
| 343 is a term as 343 = 7^3 and 344= 2^3 * 43.
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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 (jvospost3(AT)gmail.com), Sep 18 2007
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CROSSREFS
| Cf. A046099, A063528, A068781-A068784, A122692, A174113.
Sequence in context: A039400 A044003 A062376 * A204648 A202447 A202440
Adjacent sequences: A068137 A068138 A068139 * A068141 A068142 A068143
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KEYWORD
| easy,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 22 2002
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 02 2002
Title edited, cross-references added by Matthew Vandermast (ghodges14(AT)comcast.net), Dec 09 2010
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