OFFSET
1,1
COMMENTS
A subsequence of A023197 (numbers n such that sigma(n) >= 3n) which is in turn a subsequence of the abundant numbers A005101, i.e., numbers n with sigma(n)/n > 2.
Differs from A023197 from a(565) on: The first term of A023197 which is not in this sequence is A023197(565) = 27720 = A023198(1) = A023199(4), the least number with abundancy >= 4.
Numbers with abundancy sigma(n)/n < 2 are called deficient and listed in A005100. Numbers with sigma(n)/n in the interval [2,3) are listed in A204829. Numbers with sigma(n)/n in the interval [4,5) are listed in A230608. - M. F. Hasler, Dec 05 2013
A119240(3) = 1018976683725 is the least odd term in this sequence. - Amiram Eldar, Oct 31 2025
The asymptotic density d of this sequence is the densities difference of A068403 and A068404 (see the comments sections of these two sequences for bounds): 0.0179 < d < 0.0214. The numbers of terms that do not exceed 10^k, for k = 1, 2, ..., are 0, 0, 16, 195, 2009, 19943, 199678, 1991444, 19918728, 199316485, ... . Apparently, the asymptotic density of this sequence equals 0.0199... . - Amiram Eldar, Nov 10 2025
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000 (corrected and extended the original b-file from Jaroslav Krizek).
Eric Weisstein's World of Mathematics, Abundancy.
Eric Weisstein's World of Mathematics, Abundant Number.
EXAMPLE
Number 180 is in the sequence because sigma(180)/180 = 546/180 = 3.0333...
MATHEMATICA
A204828Q[k_] := 3 <= DivisorSigma[1, k]/k < 4;
Select[Range[3000], A204828Q] (* Paolo Xausa, Oct 31 2025 *)
PROG
(PARI) isok(k) = my(s = sigma(k, -1)); s >= 3 && s < 4; \\ Amiram Eldar, Oct 31 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 22 2012
STATUS
approved