A112623 - cp's OEIS frontend

A112623 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)!.

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	2
7	1
8	6
9	2
10	2
11	1
12	3
13	1
14	2
15	2
16	24
17	1
18	3
19	1
20	3
21	2
22	2
23	1
24	7
25	2
26	2
27	6
28	3
29	1
30	3
31	1
32	120
33	2
34	2
35	2
36	4
37	1
38	2
39	2
40	7
41	1
42	3
43	1
44	3
45	3
46	2
47	1
48	25
49	2
50	3
51	2
52	3
53	1
54	7
55	2
56	7
57	2
58	2
59	1
60	4
61	1
62	2
63	3
64	720
65	2
66	3
67	1
68	3
69	2
70	3
71	1
72	8
73	1
74	2
75	3
76	3
77	2
78	3
79	1
80	25
81	24
82	2
83	1
84	4
85	2
86	2
87	2
88	7
89	1
90	4
91	2
92	3
93	2
94	2
95	2
96	121
97	1
98	3
99	3
100	4
101	1

[0, 1, 1, 2, 1, 2, 1, 6, 2, 2, 1, 3, 1, 2, 2, 24, 1, 3, 1, 3, 2, 2, 1, 7, 2, 2, 6, 3, 1, 3, 1, 120, 2, 2, 2, 4, 1, 2, 2, 7, 1, 3, 1, 3, 3, 2, 1, 25, 2, 3, 2, 3, 1, 7, 2, 7, 2, 2, 1, 4, 1, 2, 3, 720, 2, 3, 1, 3, 2, 3, 1, 8, 1, 2, 3, 3, 2, 3, 1, 25, 24, 2, 1, 4, 2, 2, 2, 7, 1, 4, 2, 3, 2, 2, 2, 121, 1, 3, 3, 4, 1]

cp's OEIS Frontend

A112623 If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)!.

Table of values

List of values

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	2
7	1
8	6
9	2
10	2
11	1
12	3
13	1
14	2
15	2
16	24
17	1
18	3
19	1
20	3
21	2
22	2
23	1
24	7
25	2
26	2
27	6
28	3
29	1
30	3
31	1
32	120
33	2
34	2
35	2
36	4
37	1
38	2
39	2
40	7
41	1
42	3
43	1
44	3
45	3
46	2
47	1
48	25
49	2
50	3
51	2
52	3
53	1
54	7
55	2
56	7
57	2
58	2
59	1
60	4
61	1
62	2
63	3
64	720
65	2
66	3
67	1
68	3
69	2
70	3
71	1
72	8
73	1
74	2
75	3
76	3
77	2
78	3
79	1
80	25
81	24
82	2
83	1
84	4
85	2
86	2
87	2
88	7
89	1
90	4
91	2
92	3
93	2
94	2
95	2
96	121
97	1
98	3
99	3
100	4
101	1

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	2
7	1
8	6
9	2
10	2
11	1
12	3
13	1
14	2
15	2
16	24
17	1
18	3
19	1
20	3
21	2
22	2
23	1
24	7
25	2
26	2
27	6
28	3
29	1
30	3
31	1
32	120
33	2
34	2
35	2
36	4
37	1
38	2
39	2
40	7
41	1
42	3
43	1
44	3
45	3
46	2
47	1
48	25
49	2
50	3
51	2
52	3
53	1
54	7
55	2
56	7
57	2
58	2
59	1
60	4
61	1
62	2
63	3
64	720
65	2
66	3
67	1
68	3
69	2
70	3
71	1
72	8
73	1
74	2
75	3
76	3
77	2
78	3
79	1
80	25
81	24
82	2
83	1
84	4
85	2
86	2
87	2
88	7
89	1
90	4
91	2
92	3
93	2
94	2
95	2
96	121
97	1
98	3
99	3
100	4
101	1

n	a(n)
1	0
2	1
3	1
4	2
5	1
6	2
7	1
8	6
9	2
10	2
11	1
12	3
13	1
14	2
15	2
16	24
17	1
18	3
19	1
20	3
21	2
22	2
23	1
24	7
25	2
26	2
27	6
28	3
29	1
30	3
31	1
32	120
33	2
34	2
35	2
36	4
37	1
38	2
39	2
40	7
41	1
42	3
43	1
44	3
45	3
46	2
47	1
48	25
49	2
50	3
51	2
52	3
53	1
54	7
55	2
56	7
57	2
58	2
59	1
60	4
61	1
62	2
63	3
64	720
65	2
66	3
67	1
68	3
69	2
70	3
71	1
72	8
73	1
74	2
75	3
76	3
77	2
78	3
79	1
80	25
81	24
82	2
83	1
84	4
85	2
86	2
87	2
88	7
89	1
90	4
91	2
92	3
93	2
94	2
95	2
96	121
97	1
98	3
99	3
100	4
101	1