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 A355030 #10 Jun 22 2022 02:32:55
%S A355030 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,5,1,4,1,4,2,2,1,7,2,2,3,4,1,5,1,7,2,2,
%T A355030 2,8,1,2,2,6,1,5,1,4,4,2,1,11,2,4,2,4,1,7,2,7,2,2,1,11,1,2,4,11,2,5,1,
%U A355030 4,2,5,1,14,1,2,4,4,2,5,1,11,5,2,1,11,2
%N A355030 a(n) is the number of possible values of the number of prime divisors (counted with multiplicity) of numbers with n divisors.
%C A355030 First differs from A305254 at n = 40, from A001055 and A252665 at n = 36, from A218320 at n = 32 and from A317791, A318559 and A326334 at n = 30.
%H A355030 Amiram Eldar, <a href="/A355030/b355030.txt">Table of n, a(n) for n = 1..10000</a>
%F A355030 a(n) <= A001055(n).
%F A355030 a(p) = 1 for p prime.
%F A355030 a(A355031(n)) = n.
%e A355030 a(2) = 1 since numbers with 2 divisors are primes, i.e., numbers k with the single value Omega(k) = 1.
%e A355030 a(4) = 2 since numbers with 4 divisors are either of the following 2 forms: p1 * p2 with p1 and p2 being distinct primes, or of the form p^3 with p prime.
%e A355030 a(8) = 3 since numbers with 8 divisors are either of the following 3 forms: p1 * p2 * p3 with p1, p2 and p3 being distinct primes, p1 * p2^3, or p1^7.
%t A355030 Table[Length[Union[Total[#-1]& /@ f[n]]], {n, 1, 100}] (* using the function f by _T. D. Noe_ at A162247 *)
%Y A355030 Row lengths of A355029.
%Y A355030 Cf. A000005, A001222, A118914, A162247, A355027.
%Y A355030 Cf. A001055, A218320, A305254, A317791, A318559, A326334.
%K A355030 nonn
%O A355030 1,4
%A A355030 _Amiram Eldar_, Jun 16 2022