%I #10 Jun 22 2022 02:29:55
%S 1,1,1,1,1,1,1,1,2,2,2,3,3,4,4,4,5,5,5,6,6,7,9,9,11,12,13,14,16,17,19,
%T 23,26,30,32,35,38,40,43,51,56,62,68,74,80,86,94,106,118,128,140,152,
%U 167,179,197,221,247,272,298,325,353,384,425,473,522,567,631
%N a(n) is the maximum number of distinct prime signatures of numbers with n prime divisors (counted with multiplicity) that have the same number of divisors.
%H Amiram Eldar, <a href="/A355028/b355028.txt">Table of n, a(n) for n = 0..90</a>
%e a(8) = 2 since there are 2 prime signatures of numbers k with Omega(k) = 8, p1^5 * p2 * p3 * p4 and p1^3 * p2^3 * p3^2, that correspond to the same number of divisors, 48.
%t a[n_] := Max[Tally[Times @@ (# + 1) & /@ IntegerPartitions[n]][[;; , 2]]]; Array[a, 50, 0]
%Y Cf. A000005, A001222, A101296, A118914, A355026, A355027.
%K nonn
%O 0,9
%A _Amiram Eldar_, Jun 16 2022