This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379271 #20 May 22 2025 12:38:21
%S A379271 4,6,8,9,10,12,15,16,18,20,21,24,25,27,28,30,32,33,35,36,39,40,42,44,
%T A379271 45,48,49,50,51,52,54,55,56,57,60,63,64,65,66,68,70,72,75,76,77,78,80,
%U A379271 81,84,85,88,90,91,92,95,96,98,99,100,102,104,105,108,110,112,114,115,116,117,119,120,121,124,125,126,128
%N A379271 Composite numbers, k, whose prime factors, viewed on a log log scale, have a small standard deviation defined with respect to bigomega(k), as specified in the comments.
%C A379271 Composite numbers k (written as a product of primes p_1 * p_2 * ... * p_m) such that s( {log(log(p_i)) : 1 <= i <= m} ) < s( {i : 1 <= i <= m} ), where s is standard deviation and m = bigomega(k).
%C A379271 Loosely described, these are numbers whose prime factors, including repetitions, are relatively close together. (Note we get the same criterion irrespective of whether s is sample standard deviation or population standard deviation.)
%C A379271 The author's intent is to divide the set of composite numbers into 2 parts whose asymptotic densities differ at most by a small factor. So his choice of criterion was guided by particular information relating to the statistics of prime factors of large numbers.
%C A379271 From _Charles R Greathouse IV_, May 19 2025: (Start)
%C A379271 For example, semiprimes p*q with p <= q are in this sequence if (and only if) q < p^e where e = 2.71... is the base of the natural logarithm.
%C A379271 For any m, there are finitely many primes p (perhaps none) such that p*m is in the sequence. (End)
%t A379271 Select[Select[Range[128], CompositeQ], Less @@ Map[StandardDeviation, Transpose@ MapIndexed[{Log@ Log[#1], First[#2]} &, Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#] ] ] ] &] (* _Michael De Vlieger_, May 04 2025 *)
%Y A379271 Subsequences: A251728, the composites in A253784, A380438.
%K A379271 nonn
%O A379271 1,1
%A A379271 _Peter Munn_, Feb 18 2025