A204829 Numbers k with abundancy 2 <= sigma(k)/k < 3.

6, 12, 18, 20, 24, 28, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 104, 108, 112, 114, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 246, 252

Offset

1,1

Comments

Supersequence of (any k)-deficient-3-perfect number sequence (see Comments in A386213). Initial terms of (a(n)) which are not (any k)-deficient-3-perfect numbers are: 174, 186, 222, 246, 258, 282, 318, 354, 366, 402,... - Lechoslaw Ratajczak, Oct 24 2025

The asymptotic density d of this sequence is the densities difference of A005101 and A068403 (see A302991 and the comments section of A068403 for bounds): 0.226 < d < 0.230. The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 1, 24, 233, 2297, 22777, 227373, 2274554, 22743863, 227437606, 2274382277, ... . Apparently, the asymptotic density of this sequence equals 0.22743... . - Amiram Eldar, Nov 10 2025

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Jaroslav Krizek).

Eric Weisstein's World of Mathematics, Abundancy.

Eric Weisstein's World of Mathematics, Abundant Number.

Example

Number 70 is in sequence because sigma(70) / 70 = 144 / 70, which is between 2 and 3.

Mathematica

A204829Q[k_] := 2 <= DivisorSigma[1, k]/k < 3;
Select[Range[300], A204829Q] (* Paolo Xausa, Oct 31 2025 *)

Prog

(PARI) isok(k) = my(s = sigma(k, -1)); s >= 2 && s < 3; \\ Amiram Eldar, Oct 31 2025

Crossrefs

Cf. A005101, A068403, A204828, A230608, A302991, A386213, A386317.

Supersequence of A000396.

Sequence in context: A177052 A023196 A376880 * A005835 A007620 A100715

Adjacent sequences: A204826 A204827 A204828 * A204830 A204831 A204832

Keyword

nonn

Author

Jaroslav Krizek, Jan 22 2012

Status

approved