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 A359636 #25 Nov 03 2023 06:29:58
%S A359636 7,19,643,51427,8083633,1077940147,75582271489,34710483181813
%N A359636 a(n) is the least odd prime not in A001359 such that all subsequent composites in the gap up to the next prime have at least n distinct prime factors.
%C A359636 a(9) <= 76340177205657727, a(10) <= 225096507194749219819. - _David A. Corneth_, Jan 12 2023
%H A359636 Nilotpal Kanti Sinha, <a href="https://mathoverflow.net/questions/414186/are-there-highly-composite-prime-gaps">Are there highly composite prime gaps?</a> Question in mathoverflow, with an answer by Terry Tao, Jan 19 2022.
%e A359636 a(1) = 7: trivially, the 3 composites 8 = 2^3, 9 = 3^2, 10 = 2*5, have at least one distinct prime factor;
%e A359636 a(2) = 19: 20 = 2^2*5, 21 = 3*7, 22 = 2*11 all have 2 distinct prime factors;
%e A359636 a(3) = 643: 644 = 2^2*7*23, 645 = 3*5*43, 646 = 2*17*19, 647 is prime.
%o A359636 (PARI) a359636(maxp) = {my (k=1, pp=3); forprime (p=5, maxp, my(mi=oo); if (p-pp>2, for (j=pp+1, p-1, my(mo=omega(j)); if (mo<k, mi=0; break); mi=min(mo,mi)); if (mi>=k, print1(pp,", "); k++)); pp=p)};
%o A359636 a359636(10^7)
%Y A359636 Cf. A001359, A075590, A185032.
%K A359636 nonn,hard,more
%O A359636 1,1
%A A359636 _Hugo Pfoertner_, Jan 12 2023
%E A359636 a(8) from _Martin Ehrenstein_, Nov 03 2023