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A189228 Superabundant numbers (A004394) that are not colossally abundant (A004490). 5
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

T. D. Noe, Table of n, a(n) for n = 1..1000

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: A166727 A229295 A007544 * A048188 A121024 A120622

Adjacent sequences:  A189225 A189226 A189227 * A189229 A189230 A189231

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Jun 07 2011

STATUS

approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)