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

Author

Jonathan Sondow, Jun 07 2011

Keywords

• nonn

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).