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Search: id:A164829
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| A164829 |
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a(1) = 2; a(n) for n > 1 is the smallest k > a(n-1) such that the harmonic mean of the divisors of k is one of the previous terms a(1), ..., a(n-1). |
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1
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OFFSET
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1,1
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COMMENT
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The harmonic mean of the divisors of k is k*A000005(k)/A000203(k). a(n) for n > 1 is a harmonic number, a term of A001599. Is the sequence finite ?
Similar sequences are obtained for other values of a(1). E.g. a(1) = 5 gives 5, 140, 496, 164989440, 28103080287744; a(1) = 8 gives 8, 672, 183694492800, 7322605472000.
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LINKS
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Takeshi Goto, Table of A001599(n) for n=1..937
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EXAMPLE
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The smallest number with harmonic mean of divisors = 2 is 6, hence a(2) = 6.
The next number with harmonic mean of divisors in {2, 6} is 270, hence a(3) = 270.
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CROSSREFS
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Cf. A000005 (sigma_0, number of divisors), A000203 (sigma, sum of divisors), A001599 (harmonic or Ore numbers).
Sequence in context: A100359 A052342 A007190 this_sequence A028337 A135014 A092024
Adjacent sequences: A164826 A164827 A164828 this_sequence A164830 A164831 A164832
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KEYWORD
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nonn,hard,more
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AUTHOR
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Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 27 2009
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EXTENSIONS
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Edited and listed terms verified (using Takeshi Goto's list) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 04 2009
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