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

1,1

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.

Links

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

Formula

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

Example

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}.

Mathematica

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

Crossrefs

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

Sequence in context: A372208 A018863 A003998 * A230400 A001239 A184088

Adjacent sequences: A335541 A335542 A335543 * A335545 A335546 A335547

Keyword

nonn

Author

Amiram Eldar, Jun 13 2020

Status

approved