A023197 Numbers k such that sigma(k) >= 3*k.

120, 180, 240, 360, 420, 480, 504, 540, 600, 660, 672, 720, 780, 840, 900, 960, 1008, 1080, 1200, 1260, 1320, 1344, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Sometimes called 3-abundant numbers (but compare the comments in A033880). The first odd number is A119240(3) = 1018976683725. - T. D. Noe, Mar 31 2011

References

• Melvyn B. Nathanson, Elementary Methods in Number Theory, Springer, 2000, p 260.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• Richard Laatsch, Measuring the Abundancy of Integers, Mathematics Magazine, Vol. 59, No. 2 (1986), pp. 84-92, alternative link.

Crossrefs

Cf. A000203, A001221, A119240.

See A033880 for definition of k-abundancy.

Programs

Maple

select(t -> numtheory:-sigma(t) >= 3*t, [$1..10000]); # Robert Israel, Dec 28 2014

Mathematica

Select[Range[10000], DivisorSigma[1,#] >= 3*#&] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2010 *)

Formula

A001221(a(n)) >= 3 (Laatsch, 1986). - Amiram Eldar, Nov 07 2020