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Search: id:A039833
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| A039833 |
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Smallest of three consecutive square-free numbers n, n+1, n+2 of the form p*q where p and q are primes. |
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+0
6
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| 33, 85, 93, 141, 201, 213, 217, 301, 393, 445, 633, 697, 921, 1041, 1137, 1261, 1345, 1401, 1641, 1761, 1837, 1893, 1941, 1981, 2101, 2181, 2217, 2305, 2361, 2433, 2461, 2517, 2641, 2721, 2733, 3097, 3385, 3601, 3693, 3865, 3901, 3957, 4285, 4413, 4533, 4593, 4881, 5601
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Equivalently: n, n+1 and n+2 all have 4 divisors.
There cannot be four consecutive square-free numbers as one of them is divisible by 2^2 =4.
These 3 consecutive square-free numbers of form pq have altogether 6 prime-factors always including 2 and 3. E.g. if n=99985, the six prime-factors are {2,3,5,19997,33329,49993}. The middle term is even and not divisible by 3.
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REFERENCES
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D. Wells, Curious and interesting numbers, Penguin Books.
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EXAMPLE
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33, 34 and 35 all have 4 divisors. 85 is a term as 85 = 17*5, 86 = 43*2, 87 = 29*3.
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MATHEMATICA
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f[n_] := Plus @@ Transpose[ FactorInteger[n]] [[2]]; Select[Range[10^4], f[ # ] == f[ # + 1] == f[ # + 2] == 2 & ]
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CROSSREFS
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Cf. A038456, A039832, A008683, A007675, A063736, A063838, A070552, A045939, A056809.
Sequence in context: A052214 A063838 A075039 this_sequence A080700 A080200 A067705
Adjacent sequences: A039830 A039831 A039832 this_sequence A039834 A039835 A039836
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KEYWORD
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nonn,nice
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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EXTENSIONS
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Additional comments from Amarnath Murthy, Vladeta Jovovic, Labos E., and Benoit Cloitre, May 08 2002
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