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 A356224 #8 Aug 08 2022 16:02:47
%S A356224 1,2,1,3,1,3,1,4,1,2,1,5,1,2,1,5,1,4,1,3,1,2,1,7,1,2,1,3,1,4,1,6,1,2,
%T A356224 1,7,1,2,1,4,1,3,1,3,1,2,1,9,1,2,1,3,1,5,1,4,1,2,1,7,1,2,1,7,1,3,1,3,
%U A356224 1,2,1,10,1,2,1,3,1,3,1,5,1,2,1,5,1,2,1
%N A356224 Number of divisors of n whose prime indices cover an initial interval of positive integers.
%C A356224 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e A356224 The a(n) gapless divisors of n = 1..24:
%e A356224 1 2 1 4 1 6 1 8 1 2 1 12 1 2 1 16 1 18 1 4 1 2 1 24
%e A356224 1 2 2 4 1 6 1 8 6 2 1 12
%e A356224 1 1 2 4 4 2 1 8
%e A356224 1 2 2 1 6
%e A356224 1 1 4
%e A356224 2
%e A356224 1
%e A356224 For example, the divisors of 12 are {1,2,3,4,6,12}, of which {1,2,4,6,12} belong to A055932, so a(12) = 5.
%t A356224 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A356224 normQ[m_]:=m=={}||Union[m]==Range[Max[m]];
%t A356224 Table[Length[Select[Divisors[n],normQ[primeMS[#]]&]],{n,100}]
%Y A356224 These divisors belong to A055932, a subset of A073491 (complement A073492).
%Y A356224 The complement is A356225.
%Y A356224 A001223 lists the prime gaps.
%Y A356224 A328338 has third-largest divisor prime.
%Y A356224 A356226 gives the lengths of maximal gapless intervals of prime indices.
%Y A356224 Cf. A000005, A001222, A028334, A029709, A055874, A056239, A070824, A112798, A119313, A137921, A287170, A289509, A356223.
%K A356224 nonn
%O A356224 1,2
%A A356224 _Gus Wiseman_, Aug 04 2022