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A189228 Superabundant numbers (A004394) that are not colossally abundant (A004490). 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.)
LINKS
CROSSREFS
Cf. A112974 (Number of superabundant numbers between two consecutive colossally abundant numbers) and A166735 (Superabundant numbers that are not highly composite).
Sequence in context: A229295 A007544 A333655 * A338786 A363218 A048188
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jun 07 2011
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)