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A095849
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Numbers j where sigma_k(j) increases to a record for all real values of k.
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4
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1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 840, 1680, 2520, 5040, 10080, 15120, 25200, 27720, 55440, 110880, 166320, 277200, 720720, 1441440, 2162160, 3603600, 7207200, 10810800, 36756720, 61261200, 122522400, 183783600, 698377680
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OFFSET
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1,2
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COMMENTS
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For any value of k, sigma_k(j) > sigma_k(m) for all m < j, where the function sigma_k(j) is the sum of the k-th powers of all divisors of j.
Conjecture: a number is in this sequence if and only if it is in both A002182 and A095848. - J. Lowell, Jun 21 2008
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LINKS
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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(j) where k equals 1, 0 and -1 respectively. See also A095848.
Cf. also A166981 (numbers that establish records for both k=0 and k=-1).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Removed keyword "fini", since it appears that as yet there is no proof. - N. J. A. Sloane, Sep 17 2022
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STATUS
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approved
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