A335544 Numbers with more abundant divisors than deficient divisors.

216, 240, 288, 360, 432, 480, 504, 540, 576, 600, 648, 672, 720, 792, 840, 864, 936, 960, 972, 1008, 1056, 1080, 1120, 1152, 1200, 1248, 1260, 1296, 1320, 1344, 1440, 1512, 1560, 1584, 1620, 1680, 1728, 1800, 1872, 1920, 1944, 2016, 2112, 2160, 2240, 2268, 2304

Offset: 1

Author

Amiram Eldar, Jun 13 2020

Keywords

• nonn

Comments

This sequence is infinite. For example, 216*p is a term for all primes p.

The least odd term of this sequence is a(16317321) = 638512875.

Apparently, this sequence has an asymptotic density of about 0.025.

Examples

			216 is a term since it has 8 abundant divisors, {12, 18, 24, 36, 54, 72, 108, 216}, and only 7 deficient divisors, {1, 2, 3, 4, 8, 9, 27}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A005100, A005101, A080224, A080226, A335543.

Programs

Mathematica

ab[n_] := DivisorSigma[1, n] - 2n; moreAbQ[n_] := Count[(abs = ab/@Divisors[n]), ?(# > 0 &)] > Count[abs, ?(# < 0 &)]; Select[Range[50000], moreAbQ]

Formula

Numbers k such that A080224(k) > A080226(k).