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

1,1

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

3-nondeficient numbers (in analogy with A023196) would be a more logical name, with 3-abundant numbers being A068403. - Antti Karttunen, Sep 16 2025

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.

Eric Weisstein's World of Mathematics, Abundancy.

Formula

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

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 *)

Crossrefs

Cf. A000203, A001221, A119240.

See A033880 for definition of k-abundancy.

Subsequence of A023196 (sigma(k) >= 2*k).

Disjoint union of A005820 (3-perfect) and A068403 (3-abundant numbers).

Other subsequences: A023198 (sigma(k) >= 4*k), A204828, A204830, A206025, A215264 (sigma(k) > 5*k), A291457, A306476, A307112, A388019 (primitive terms), A388022, A388024, A388026, A388036.

Complement is (A005100 U A204829). See also A307122.

Cf. also analogous sequences A285615, A300664 (also a subsequence), A328135.

Sequence in context: A232461 A090782 A337386 * A204828 A204830 A388036

Adjacent sequences: A023194 A023195 A023196 * A023198 A023199 A023200

Keyword

nonn

Author

David W. Wilson

Status

approved