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Search: id:A140798
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| A140798 |
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Harmonic numbers that are not multiply-perfect. |
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+0
1
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| 1, 140, 270, 1638, 2970, 6200, 8190, 18600, 18620, 27846, 55860, 105664, 117800, 167400, 173600, 237510, 242060, 332640, 360360, 539400, 695520, 726180, 753480, 950976, 1089270, 1421280, 1539720, 2229500, 2290260, 2457000, 2845800, 4358600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For n>0, sequence is A001599 excluding those entries that appear in A007691.
Multiply-perfect numbers m (with sigma(m)/m an integer) are necessarily harmonic numbers (with tau(m)/{sigma(m)/m } an integer), but the converse is not true : If m divides sigma(m), then quotient sigma(m)/m divides tau(m) [m =A007691]; However, quotient tau(n)/{sigma(n)/n} being an integer does not imply quotient sigma(n)/n is necessarily an integer [n=A001599].
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 140, pp 48, Ellipses, Paris 2008.
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CROSSREFS
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Cf. A000203, A054030, A000005.
Sequence in context: A114825 A131492 A090945 this_sequence A010080 A133711 A128193
Adjacent sequences: A140795 A140796 A140797 this_sequence A140799 A140800 A140801
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 15 2008
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