A039725 Even abundant numbers divided by 2. (Formerly N1690)

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

1,1

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

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A177201 A090466 A090428 * A262362 A125494 A177029

Adjacent sequences: A039722 A039723 A039724 * A039726 A039727 A039728

Keyword

easy,nonn

Author

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

Extensions

Corrected and edited by Daniel Forgues, Nov 22 2010

Status

approved