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 A382327 #16 Apr 02 2025 20:36:51
%S A382327 4,8,12,24,36,48,60,72,120,144,180,240,288,360,480,576,720,1080,1440,
%T A382327 2160,2520,2880,3600,4320,5040,7200,7560,8640,10080,14400,15120,20160,
%U A382327 25200,30240,40320,50400,60480,80640,90720,100800,120960,151200,181440,201600
%N A382327 Numbers with a record ratio of proper factorizations to prime factors (counted with multiplicity).
%C A382327 Numbers k that give a record value for A028422(k)/A001222(k).
%C A382327 a(n) = 0 (mod 4), and with prime factors of terms clustering around the smallest primes, it is observed that as n increases, the gcd of a(n)..a(oo) remains among the largest divisors of a(n).
%e A382327 a(1) = 4: |{{2, 2}}| / |{2, 2}| = 1/2.
%e A382327 a(2) = 8: |{{2, 2, 2}, {2, 4}}| / |{2, 2, 2}| = 2/3.
%e A382327 a(3) = 12: |{{2, 2, 3}, {2, 6}, {3, 4}}| / |{2, 2, 3}| = 3/3.
%o A382327 (PARI) f_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, return(if(#f, 1, 0))); my(d, c=0); fordiv(r, d, if(d==1 || d==x || (#f && d<f[#f]), next); listput(f, d); c+=f_count(x, f); listpop(f)); return(c)}
%o A382327 my(mx=0); for(x=2, 10^6, my(m=f_count(x)/bigomega(x)); if(m>mx, mx=m; print1(x, ", ")))
%Y A382327 Cf. A028422, A001222, A033833, A382325, A382326.
%Y A382327 Subsequence of A025487.
%K A382327 nonn
%O A382327 1,1
%A A382327 _Charles L. Hohn_, Mar 21 2025