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Superabundant numbers (A004394) that are not colossally abundant (A004490).
8

%I #10 Mar 30 2012 19:00:09

%S 1,4,24,36,48,180,240,720,840,1260,1680,10080,15120,25200,27720,

%T 110880,166320,277200,332640,554400,665280,2162160,3603600,7207200,

%U 8648640,10810800,36756720,61261200,73513440,122522400,147026880,183783600,698377680,735134400

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

%C 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.)

%H T. D. Noe, <a href="/A189228/b189228.txt">Table of n, a(n) for n = 1..1000</a>

%Y Cf. A112974 (Number of superabundant numbers between two consecutive colossally abundant numbers) and A166735 (Superabundant numbers that are not highly composite).

%K nonn

%O 1,2

%A _Jonathan Sondow_, Jun 07 2011