A superabundant number is a positive integer 
such that 
for all positive
integers 
,
where 
is the divisor function giving the sum
of the positive divisors of 
(Alaoglu and Erdős 1944, p. 450). Superabundant
numbers are closely related to highly composite
numbers, and the first 19 superabundant and highly composite numbers are the
same. The first few are 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720,
840, 1260, ... (OEIS A004394).
Superabundant Number
See also
Highly Composite NumberExplore with Wolfram|Alpha
References
Alaoglu, L. and Erdős, P. "On Highly Composite and Similar Numbers." Trans. Amer. Math. Soc. 56, 448-469, 1944. https://doi.org/10.1090/s0002-9947-1944-0011087-2.Honsberger, R. Mathematical Gems I. Washington, DC: Math. Assoc. Amer., p. 112, 1973.Honsberger, R. "An Introduction to Ramanujan's Highly Composite Numbers." Ch. 14 in Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 193-207, 1985.Sloane, N. J. A. Sequence A004394 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. New York: Penguin Books, pp. 85 and 128, 1986.Referenced on Wolfram|Alpha
Superabundant NumberCite this as:
Weisstein, Eric W. "Superabundant Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SuperabundantNumber.html