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

1,3

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.

Links

Table of n, a(n) for n=1..53.

Formula

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

Example

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.

Sequence in context: A036706 A336785 A080739 * A242065 A056424 A050324

Adjacent sequences: A361662 A361663 A361664 * A361666 A361667 A361668

Keyword

nonn

Author

Pontus von Brömssen, Mar 20 2023

Status

approved