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A189228
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Superabundant numbers (A004394) that are not colossally abundant (A004490).
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8
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1, 4, 24, 36, 48, 180, 240, 720, 840, 1260, 1680, 10080, 15120, 25200, 27720, 110880, 166320, 277200, 332640, 554400, 665280, 2162160, 3603600, 7207200, 8648640, 10810800, 36756720, 61261200, 73513440, 122522400, 147026880, 183783600, 698377680, 735134400
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OFFSET
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1,2
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COMMENTS
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All colossally abundant (CA) numbers are also superabundant (SA). (Proof. If n is CA and k < n, then sigma(n)/n = n^{epsilon}*sigma(n)/n^{1+epsilon} >= n^{epsilon}*sigma(k)/k^{1+epsilon} > k^{epsilon}*sigma(k)/k^{1+epsilon} = sigma(k)/k, and so n is SA.)
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LINKS
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CROSSREFS
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Cf. A112974 (Number of superabundant numbers between two consecutive colossally abundant numbers) and A166735 (Superabundant numbers that are not highly composite).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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