A361665 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.

1, 1, 2, 3, 4, 8, 8, 13, 26, 20, 16, 44, 32, 48, 76, 75, 64, 176, 128, 132, 208, 112, 256, 308, 252, 256, 818, 368, 512, 604, 1024, 541, 544, 576, 768, 1460, 2048, 1280, 1376, 1076, 4096, 1888, 8192, 976, 3172, 2816, 16384, 2612, 2568, 2316, 3392, 2496, 32768

Offset: 1

Author

Pontus von Brömssen, Mar 20 2023

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A074206, A181821, A361666.

Formula

a(n) = A074206(A181821(n)).