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A256384 Number A(n,k) of factorizations of m^n into at most n factors, where m is a product of exactly k distinct primes; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Table of values

n a(n)
0 1
1 1
2 1
3 1
4 1
5 1
6 1
7 1
8 2
9 1
10 1
11 1
12 5
13 3
14 1
15 1
16 1
17 14
18 19
19 5
20 1
21 1
22 1
23 41
24 171
25 74
26 7
27 1
28 1
29 1
30 122
31 1675
32 1975
33 248
34 11
35 1
36 1
37 1
38 365
39 16683
40 64182
41 20096
42 814
43 15
44 1
45 1
46 1
47 1094
48 166699
49 2203215
50 2213016
51 187921
52 2457
53 22
54 1
55 1
56 1
57 3281
58 1666731
59 76727374
60 268446852
61 69406700
62 1609727
63 7168
64 30
65 1

List of values

[1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 14, 19, 5, 1, 1, 1, 41, 171, 74, 7, 1, 1, 1, 122, 1675, 1975, 248, 11, 1, 1, 1, 365, 16683, 64182, 20096, 814, 15, 1, 1, 1, 1094, 166699, 2203215, 2213016, 187921, 2457, 22, 1, 1, 1, 3281, 1666731, 76727374, 268446852, 69406700, 1609727, 7168, 30, 1]