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Search: id:A144146
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| A144146 |
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A positive integer n is included if every nonzero exponent in the prime-factorization of n is coprime to n. |
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+0
2
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| 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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1 is included somewhat arbitrarily. 1 has no nonzero exponents in its prime factorization, but it also has no prime-factorization exponents that are non-coprime to 1.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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40 has the prime-factorization 2^3 * 5^1. The exponents are therefore 3 and 1. Since both 3 and 1 are coprime to 40, then 40 is included in the sequence.
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MATHEMATICA
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Select[Range[100], GCD[Times @@ Table[FactorInteger[ # ][[i, 2]], {i, 1, Length[FactorInteger[ # ]]}], # ] == 1 &] [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Sep 15 2008]
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CROSSREFS
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Sequence in context: A047588 A039213 A119605 this_sequence A090240 A137407 A167209
Adjacent sequences: A144143 A144144 A144145 this_sequence A144147 A144148 A144149
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Sep 11 2008
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Sep 15 2008
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