A039725 Even abundant numbers divided by 2.

6, 9, 10, 12, 15, 18, 20, 21, 24, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 51, 52, 54, 56, 57, 60, 63, 66, 69, 70, 72, 75, 78, 80, 81, 84, 87, 88, 90, 93, 96, 98, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 117, 120, 123, 126, 129, 130, 132, 135, 136

Offset: 1

Author

N. J. A. Sloane. This was included in the 1973 "Handbook", but was then dropped from the database. Resubmitted by James Sellers. Entry revised by N. J. A. Sloane, Jun 12 2012

Keywords

• easy
• nonn

Comments

While the first even abundant number is 12 = 2^2*3, the first odd abundant is 945 = 3^3*5*7, the 232nd abundant number!

The asymptotic density of this sequence is in the interval (0.491096, 0.491156) (based on the known bounds on the densities of A005101 and A005231; see A302991 and A322287). - Amiram Eldar, Mar 11 2024

Examples

			The first even abundant number is 12, so 12/2 = 6 is the first element in this sequence.
		

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101, A005231, A173490, A302991, A322287.

Programs

Mathematica

Select[Range[2,300,2],DivisorSigma[1,#]>2*#&]/2 (* Harvey P. Dale, Mar 22 2020 *)

Formula

a(n) = A173490(n) / 2.

Extensions

Corrected and edited by Daniel Forgues, Nov 22 2010