A319071 - cp's OEIS frontend

A319071 Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity.

n	a(n)
0	1
1	0
2	0
3	0
4	2
5	0
6	2
7	0
8	3
9	2
10	3
11	0
12	4
13	1
14	4
15	3
16	7
17	1
18	7
19	1
20	8
21	6
22	8
23	0
24	15
25	5
26	12
27	6
28	15
29	4
30	22
31	4
32	24
33	12
34	22
35	8
36	35
37	7
38	30
39	16
40	42
41	9
42	50
43	9
44	50
45	30
46	53
47	7
48	79
49	22
50	72
51	33
52	87
53	21
54	109
55	26
56	111
57	55
58	117
59	24
60	168
61	40
62	149
63	65
64	178
65	59

[1, 0, 0, 0, 2, 0, 2, 0, 3, 2, 3, 0, 4, 1, 4, 3, 7, 1, 7, 1, 8, 6, 8, 0, 15, 5, 12, 6, 15, 4, 22, 4, 24, 12, 22, 8, 35, 7, 30, 16, 42, 9, 50, 9, 50, 30, 53, 7, 79, 22, 72, 33, 87, 21, 109, 26, 111, 55, 117, 24, 168, 40, 149, 65, 178, 59]

cp's OEIS Frontend

A319071 Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity.

Table of values

List of values

n	a(n)
0	1
1	0
2	0
3	0
4	2
5	0
6	2
7	0
8	3
9	2
10	3
11	0
12	4
13	1
14	4
15	3
16	7
17	1
18	7
19	1
20	8
21	6
22	8
23	0
24	15
25	5
26	12
27	6
28	15
29	4
30	22
31	4
32	24
33	12
34	22
35	8
36	35
37	7
38	30
39	16
40	42
41	9
42	50
43	9
44	50
45	30
46	53
47	7
48	79
49	22
50	72
51	33
52	87
53	21
54	109
55	26
56	111
57	55
58	117
59	24
60	168
61	40
62	149
63	65
64	178
65	59

n	a(n)
0	1
1	0
2	0
3	0
4	2
5	0
6	2
7	0
8	3
9	2
10	3
11	0
12	4
13	1
14	4
15	3
16	7
17	1
18	7
19	1
20	8
21	6
22	8
23	0
24	15
25	5
26	12
27	6
28	15
29	4
30	22
31	4
32	24
33	12
34	22
35	8
36	35
37	7
38	30
39	16
40	42
41	9
42	50
43	9
44	50
45	30
46	53
47	7
48	79
49	22
50	72
51	33
52	87
53	21
54	109
55	26
56	111
57	55
58	117
59	24
60	168
61	40
62	149
63	65
64	178
65	59

n	a(n)
0	1
1	0
2	0
3	0
4	2
5	0
6	2
7	0
8	3
9	2
10	3
11	0
12	4
13	1
14	4
15	3
16	7
17	1
18	7
19	1
20	8
21	6
22	8
23	0
24	15
25	5
26	12
27	6
28	15
29	4
30	22
31	4
32	24
33	12
34	22
35	8
36	35
37	7
38	30
39	16
40	42
41	9
42	50
43	9
44	50
45	30
46	53
47	7
48	79
49	22
50	72
51	33
52	87
53	21
54	109
55	26
56	111
57	55
58	117
59	24
60	168
61	40
62	149
63	65
64	178
65	59