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 A333725 #20 Jan 09 2023 19:02:47
%S A333725 0,1,1,2,4,2,4,2,13,11,11,20,56,18,59,58,105,307,284,278,528,515,501,
%T A333725 241,1684,466,456,2491,2403,4676,4561,4459,4396,12839,4202,8317,4111,
%U A333725 26274,25673,50073,48866,47998,47441,139491,45881,90692,134351,220465,173831,257677
%N A333725 Number of primes between pairs of consecutive highly composite numbers (A002182).
%H A333725 Charles R Greathouse IV, <a href="/A333725/b333725.txt">Table of n, a(n) for n = 1..200</a>
%F A333725 a(n) = A000720(A002182(n+1)) - A000720(A002182(n)) for n > 1. - _Amiram Eldar_, Apr 26 2020
%e A333725 There are no primes between HCN(1) and HCN(2), so a(1) = 0. The next term a(2) is equal to 1 as 3 is the only prime between HCN(2) and HCN(3); the prime 2 is not greater than HCN(2) and so is omitted here. The first gap to contain more than one prime occurs at a(4) = 2, which alludes to 7 and 11 being the only primes contained within HCN(4) and HCN(5).
%t A333725 Join[{0},PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[DeleteDuplicates[Table[ {n,DivisorSigma[ 0,n]},{n,2,22*10^5}],GreaterEqual[#1[[2]],#2[[2]]]&][[All,1]],2,1]] (* _Harvey P. Dale_, Jan 09 2023 *)
%Y A333725 Cf. A002182, A000720, A262501.
%K A333725 nonn
%O A333725 1,4
%A A333725 _Robin Powell_, Apr 03 2020
%E A333725 More terms from _Giovanni Resta_, Apr 04 2020