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

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

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: A229295 A007544 A333655 * A338786 A363218 A387269

Adjacent sequences: A189225 A189226 A189227 * A189229 A189230 A189231

Keyword

nonn

Author

Jonathan Sondow, Jun 07 2011

Status

approved