%I #7 Mar 24 2023 17:45:14
%S 1,1,2,3,4,8,8,13,26,20,16,44,32,48,76,75,64,176,128,132,208,112,256,
%T 308,252,256,818,368,512,604,1024,541,544,576,768,1460,2048,1280,1376,
%U 1076,4096,1888,8192,976,3172,2816,16384,2612,2568,2316,3392,2496,32768
%N Number of ordered factorizations of p_1^x_1 * ... * p_k^x_k, where (x_1, ..., x_k) is the partition with Heinz number n and p_1, ..., p_k are distinct primes.
%C Also, a(n) is the number of paths from (0, ..., 0) to P in which each step adds a nonnegative integer to each coordinate (and a positive number to at least one coordinate), where P is the partition with Heinz number n.
%F a(n) = A074206(A181821(n)).
%e The partition with Heinz number 6 is (1,2), and p^1*q^2 has 8 ordered factorizations, where p and q are distinct primes, so a(6) = 8. With p = 3 and q = 2, for example, we have the 8 = A074206(12) factorizations 12 = 2*6 = 3*4 = 4*3 = 6*2 = 2*2*3 = 2*3*2 = 3*2*2.
%Y Cf. A074206, A181821, A361666.
%K nonn
%O 1,3
%A _Pontus von Brömssen_, Mar 20 2023