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 A355027 #13 Jun 22 2022 02:33:05
%S A355027 1,1,2,3,5,7,11,15,21,29,39,49,66,84,108,136,171,211,259,320,386,468,
%T A355027 565,674,801,954,1117,1333,1556,1831,2107,2478,2838,3309,3788,4396,
%U A355027 4979,5780,6511,7506,8451,9696,10834,12429,13846,15814,17576,20030,22123,25179
%N A355027 a(n) is the number of possible values of numbers of divisors of numbers k with Omega(k) = n.
%H A355027 Amiram Eldar, <a href="/A355027/b355027.txt">Table of n, a(n) for n = 0..90</a>
%F A355027 a(n) <= A000041(n).
%e A355027 For n = 2, the numbers k with Omega(k) = 2 are either of the form p^2 with p prime, or of the form p1*p2 with p1 and p2 being distinct primes. The corresponding numbers of divisors are 3 and 4, respectively. Since there are 2 possible values, a(2) = 2.
%e A355027 For n = 8, there are 22 prime signatures of numbers k with Omega(k) = 8, corresponding to the number of partitions of 8. However, the prime signatures p1^5 * p2 * p3 * p4 and p1^3 * p2^3 * p3^2 both correspond to the same number of divisors, 48. Therefore, there are only 21 distinct possible values of the number of divisors, and a(8) = 21.
%t A355027 a[n_] := Length @ Union[Times @@ (# + 1) & /@ IntegerPartitions[n]]; Array[a, 50, 0]
%o A355027 (PARI) a(n) = { my (m=Map()); forpart(p=n, mapput(m,prod(k=1, #p, 1+p[k]),0)); #m } \\ _Rémy Sigrist_, Jun 17 2022
%Y A355027 Row lengths of A355026.
%Y A355027 Cf. A000005, A000041, A001222.
%K A355027 nonn
%O A355027 0,3
%A A355027 _Amiram Eldar_, Jun 16 2022