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Search: id:A095849
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| A095849 |
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Numbers n where sigma_k(n) increases to a record for all real values of k. |
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+0
3
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| 1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 840, 1680, 2520, 5040
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For any value of k, sigma_k(n) > sigma_k(m) for all m > n, where the function sigma_k(n) is the sum of the k-th powers of all divisors of n.
Conjecture: a number is in this sequence if and only if it is in both A002182 and A095848. - J. Lowell (jhbubby(AT)mindspring.com), Jun 21 2008
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CROSSREFS
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Cf. A002093 (highly abundant numbers), A002182 (highly composite numbers) and A004394 (superabundant numbers), consisting of numbers that establish records for sigma_k(n) where k equals 1, 0, and -1 respectively. Also see A095848.
Cf. A094783.
Sequence in context: A019505 A135614 A115387 this_sequence A094783 A058764 A087009
Adjacent sequences: A095846 A095847 A095848 this_sequence A095850 A095851 A095852
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KEYWORD
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more,nonn
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AUTHOR
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Matthew Vandermast (ghodges14(AT)comcast.net), Jun 09 2004
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