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 A075591 #12 Feb 20 2024 07:01:02
%S A075591 6,30,462,2310,43890,1138830,17160990,300690390,15651726090,
%T A075591 239378649510,12234189897930,568815710072610,19835154277048110,
%U A075591 693386350578511590,37508276737897976010,3338236629672919864890
%N A075591 Smallest squarefree number with n prime divisors which is the average of a twin prime pair.
%e A075591 a(4) = 462 because 462 = 2*3*7*11 and the twin primes are 461 and 463.
%t A075591 Generate[pIndex_, i_] := Module[{p2, t}, p2=pIndex; While[p2[[i]]++; Do[p2[[j]]=p2[[i]]+j-i, {j, i+1, Length[p2]}]; t=Times@@Prime[p2]; t<fact*base, AppendTo[s, t]; If[i<Length[p2], Generate[p2, i+1]]]]; fact=3; Table[pin=Range[n]; base=Times@@Prime[pin]; s={base}; Do[Generate[pin, j], {j, n}]; s=Sort[s]; noPrime=True; i=0; While[noPrime&&i<Length[s], i++; noPrime=!(PrimeQ[ -1+s[[i]]] && PrimeQ[1+s[[i]]])]; If[noPrime, -1, s[[i]]], {n, 2, 20}] (T. D. Noe)
%Y A075591 Cf. A075590.
%Y A075591 Cf. A073918 (least prime p such that p-1 has exactly n distinct prime factors), A098026 (least prime p such that p+1 has exactly n distinct prime factors).
%K A075591 nonn
%O A075591 2,1
%A A075591 _Amarnath Murthy_, Sep 26 2002
%E A075591 More terms from _T. D. Noe_, Dec 13 2004