A347935 Numbers k such that A187795(k) > 2*k.

60, 72, 108, 120, 144, 168, 180, 216, 240, 252, 264, 280, 288, 300, 312, 324, 336, 360, 396, 400, 420, 432, 468, 480, 504, 528, 540, 560, 576, 588, 600, 612, 624, 648, 660, 672, 684, 720, 756, 780, 792, 800, 816, 828, 840, 864, 880, 900, 912, 924, 936, 960, 972

Offset: 1

Author

Amiram Eldar, Sep 20 2021

Keywords

• nonn

Comments

Numbers k whose sum of aliquot divisors that are abundant numbers is > k.

If k is a term then all the positive multiples of k are also terms.

The smallest odd term is a(10042) = 155925.

The numbers of terms not exceeding 10^k for k = 1, 2, ... are 0, 2, 53, 629, 6423, 63932, 639947, 6395539, 63934596, ... Apparently, this sequence has an asymptotic density 0.0639...

Examples

			The divisors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}. The abundant divisors are {12, 20, 30, 60} and their sum is 122 > 2*60 = 120. Therefore, 60 is a term.
		

Links

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

Crossrefs

Subsequence of A005101.

Cf. A187795.

Programs

Mathematica

abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1000], q]

PARI

isok(k) = sumdiv(k, d, if (sigma(d)>2*d, d)) > 2*k; \\ Michel Marcus, Sep 20 2021