Decomposition of A022559 - 2D graph - First 500 terms
Sum of exponents in prime-power factorization of n!.
n |
a022559 |
weight k(n) |
level L(n) |
jump |
1 |
0 |
0 |
0 |
1 |
2 |
1 |
0 |
0 |
1 |
3 |
2 |
0 |
0 |
2 |
4 |
4 |
3 |
1 |
1 |
5 |
5 |
3 |
1 |
2 |
6 |
7 |
2 |
3 |
1 |
7 |
8 |
5 |
1 |
3 |
8 |
11 |
3 |
3 |
2 |
9 |
13 |
11 |
1 |
2 |
10 |
15 |
2 |
7 |
1 |
11 |
16 |
13 |
1 |
3 |
12 |
19 |
2 |
9 |
1 |
13 |
20 |
3 |
6 |
2 |
14 |
22 |
4 |
5 |
2 |
15 |
24 |
5 |
4 |
4 |
16 |
28 |
3 |
9 |
1 |
17 |
29 |
13 |
2 |
3 |
18 |
32 |
31 |
1 |
1 |
19 |
33 |
5 |
6 |
3 |
20 |
36 |
17 |
2 |
2 |
21 |
38 |
3 |
12 |
2 |
22 |
40 |
3 |
13 |
1 |
23 |
41 |
37 |
1 |
4 |
24 |
45 |
43 |
1 |
2 |
25 |
47 |
3 |
15 |
2 |
26 |
49 |
23 |
2 |
3 |
27 |
52 |
7 |
7 |
3 |
28 |
55 |
2 |
27 |
1 |
29 |
56 |
53 |
1 |
3 |
30 |
59 |
2 |
29 |
1 |
31 |
60 |
11 |
5 |
5 |
32 |
65 |
3 |
21 |
2 |
33 |
67 |
5 |
13 |
2 |
34 |
69 |
67 |
1 |
2 |
35 |
71 |
67 |
1 |
4 |
36 |
75 |
2 |
37 |
1 |
37 |
76 |
37 |
2 |
2 |
38 |
78 |
4 |
19 |
2 |
39 |
80 |
19 |
4 |
4 |
40 |
84 |
83 |
1 |
1 |
41 |
85 |
41 |
2 |
3 |
42 |
88 |
3 |
29 |
1 |
43 |
89 |
43 |
2 |
3 |
44 |
92 |
89 |
1 |
3 |
45 |
95 |
3 |
31 |
2 |
46 |
97 |
2 |
48 |
1 |
47 |
98 |
31 |
3 |
5 |
48 |
103 |
101 |
1 |
2 |
49 |
105 |
6 |
17 |
3 |
50 |
108 |
53 |
2 |
2 |
51 |
110 |
107 |
1 |
3 |
52 |
113 |
2 |
56 |
1 |
53 |
114 |
5 |
22 |
4 |
54 |
118 |
4 |
29 |
2 |
55 |
120 |
29 |
4 |
4 |
56 |
124 |
61 |
2 |
2 |
57 |
126 |
4 |
31 |
2 |
58 |
128 |
127 |
1 |
1 |
59 |
129 |
5 |
25 |
4 |
60 |
133 |
2 |
66 |
1 |
61 |
134 |
3 |
44 |
2 |
62 |
136 |
7 |
19 |
3 |
63 |
139 |
7 |
19 |
6 |
64 |
145 |
11 |
13 |
2 |
65 |
147 |
4 |
36 |
3 |
66 |
150 |
149 |
1 |
1 |
67 |
151 |
4 |
37 |
3 |
68 |
154 |
4 |
38 |
2 |
69 |
156 |
9 |
17 |
3 |
70 |
159 |
2 |
79 |
1 |
71 |
160 |
31 |
5 |
5 |
72 |
165 |
2 |
82 |
1 |
73 |
166 |
4 |
41 |
2 |
74 |
168 |
5 |
33 |
3 |
75 |
171 |
4 |
42 |
3 |
76 |
174 |
4 |
43 |
2 |
77 |
176 |
173 |
1 |
3 |
78 |
179 |
2 |
89 |
1 |
79 |
180 |
7 |
25 |
5 |
80 |
185 |
181 |
1 |
4 |
81 |
189 |
11 |
17 |
2 |
82 |
191 |
2 |
95 |
1 |
83 |
192 |
47 |
4 |
4 |
84 |
196 |
97 |
2 |
2 |
85 |
198 |
4 |
49 |
2 |
86 |
200 |
3 |
66 |
2 |
87 |
202 |
6 |
33 |
4 |
88 |
206 |
5 |
41 |
1 |
89 |
207 |
7 |
29 |
4 |
90 |
211 |
11 |
19 |
2 |
91 |
213 |
5 |
42 |
3 |
92 |
216 |
107 |
2 |
2 |
93 |
218 |
3 |
72 |
2 |
94 |
220 |
109 |
2 |
2 |
95 |
222 |
8 |
27 |
6 |
96 |
228 |
227 |
1 |
1 |
97 |
229 |
113 |
2 |
3 |
98 |
232 |
229 |
1 |
3 |
99 |
235 |
7 |
33 |
4 |
100 |
239 |
2 |
119 |
1 |
101 |
240 |
79 |
3 |
3 |
102 |
243 |
2 |
121 |
1 |
103 |
244 |
5 |
48 |
4 |
104 |
248 |
5 |
49 |
3 |
105 |
251 |
3 |
83 |
2 |
106 |
253 |
2 |
126 |
1 |
107 |
254 |
83 |
3 |
5 |
108 |
259 |
2 |
129 |
1 |
109 |
260 |
257 |
1 |
3 |
110 |
263 |
3 |
87 |
2 |
111 |
265 |
10 |
26 |
5 |
112 |
270 |
269 |
1 |
1 |
113 |
271 |
4 |
67 |
3 |
114 |
274 |
4 |
68 |
2 |
115 |
276 |
7 |
39 |
3 |
116 |
279 |
4 |
69 |
3 |
117 |
282 |
4 |
70 |
2 |
118 |
284 |
3 |
94 |
2 |
119 |
286 |
281 |
1 |
5 |
120 |
291 |
17 |
17 |
2 |
121 |
293 |
3 |
97 |
2 |
122 |
295 |
293 |
1 |
2 |
123 |
297 |
6 |
49 |
3 |
124 |
300 |
9 |
33 |
3 |
125 |
303 |
13 |
23 |
4 |
126 |
307 |
2 |
153 |
1 |
127 |
308 |
43 |
7 |
7 |
128 |
315 |
313 |
1 |
2 |
129 |
317 |
157 |
2 |
3 |
130 |
320 |
11 |
29 |
1 |
131 |
321 |
317 |
1 |
4 |
132 |
325 |
17 |
19 |
2 |
133 |
327 |
5 |
65 |
2 |
134 |
329 |
5 |
65 |
4 |
135 |
333 |
7 |
47 |
4 |
136 |
337 |
2 |
168 |
1 |
137 |
338 |
5 |
67 |
3 |
138 |
341 |
2 |
170 |
1 |
139 |
342 |
13 |
26 |
4 |
140 |
346 |
4 |
86 |
2 |
141 |
348 |
173 |
2 |
2 |
142 |
350 |
3 |
116 |
2 |
143 |
352 |
173 |
2 |
6 |
144 |
358 |
4 |
89 |
2 |
145 |
360 |
179 |
2 |
2 |
146 |
362 |
359 |
1 |
3 |
147 |
365 |
181 |
2 |
3 |
148 |
368 |
367 |
1 |
1 |
149 |
369 |
5 |
73 |
4 |
150 |
373 |
2 |
186 |
1 |
151 |
374 |
5 |
74 |
4 |
152 |
378 |
5 |
75 |
3 |
153 |
381 |
6 |
63 |
3 |
154 |
384 |
191 |
2 |
2 |
155 |
386 |
191 |
2 |
4 |
156 |
390 |
389 |
1 |
1 |
157 |
391 |
389 |
1 |
2 |
158 |
393 |
17 |
23 |
2 |
159 |
395 |
389 |
1 |
6 |
160 |
401 |
3 |
133 |
2 |
161 |
403 |
199 |
2 |
5 |
162 |
408 |
11 |
37 |
1 |
163 |
409 |
7 |
58 |
3 |
164 |
412 |
409 |
1 |
3 |
165 |
415 |
7 |
59 |
2 |
166 |
417 |
2 |
208 |
1 |
167 |
418 |
7 |
59 |
5 |
168 |
423 |
421 |
1 |
2 |
169 |
425 |
211 |
2 |
3 |
170 |
428 |
5 |
85 |
3 |
171 |
431 |
4 |
107 |
3 |
172 |
434 |
433 |
1 |
1 |
173 |
435 |
4 |
108 |
3 |
174 |
438 |
5 |
87 |
3 |
175 |
441 |
109 |
4 |
5 |
176 |
446 |
3 |
148 |
2 |
177 |
448 |
223 |
2 |
2 |
178 |
450 |
449 |
1 |
1 |
179 |
451 |
223 |
2 |
5 |
180 |
456 |
5 |
91 |
1 |
181 |
457 |
227 |
2 |
3 |
182 |
460 |
229 |
2 |
2 |
183 |
462 |
229 |
2 |
4 |
184 |
466 |
4 |
116 |
2 |
185 |
468 |
5 |
93 |
3 |
186 |
471 |
7 |
67 |
2 |
187 |
473 |
5 |
94 |
3 |
188 |
476 |
8 |
59 |
4 |
189 |
480 |
9 |
53 |
3 |
190 |
483 |
2 |
241 |
1 |
191 |
484 |
9 |
53 |
7 |
192 |
491 |
2 |
245 |
1 |
193 |
492 |
5 |
98 |
2 |
194 |
494 |
491 |
1 |
3 |
195 |
497 |
17 |
29 |
4 |
196 |
501 |
2 |
250 |
1 |
197 |
502 |
6 |
83 |
4 |
198 |
506 |
5 |
101 |
1 |
199 |
507 |
251 |
2 |
5 |
200 |
512 |
3 |
170 |
2 |
201 |
514 |
4 |
128 |
2 |
202 |
516 |
257 |
2 |
2 |
203 |
518 |
257 |
2 |
4 |
204 |
522 |
4 |
130 |
2 |
205 |
524 |
3 |
174 |
2 |
206 |
526 |
523 |
1 |
3 |
207 |
529 |
131 |
4 |
5 |
208 |
534 |
4 |
133 |
2 |
209 |
536 |
7 |
76 |
4 |
210 |
540 |
7 |
77 |
1 |
211 |
541 |
269 |
2 |
3 |
212 |
544 |
271 |
2 |
2 |
213 |
546 |
4 |
136 |
2 |
214 |
548 |
3 |
182 |
2 |
215 |
550 |
8 |
68 |
6 |
216 |
556 |
277 |
2 |
2 |
217 |
558 |
4 |
139 |
2 |
218 |
560 |
3 |
186 |
2 |
219 |
562 |
6 |
93 |
4 |
220 |
566 |
3 |
188 |
2 |
221 |
568 |
5 |
113 |
3 |
222 |
571 |
2 |
285 |
1 |
223 |
572 |
283 |
2 |
6 |
224 |
578 |
7 |
82 |
4 |
225 |
582 |
4 |
145 |
2 |
226 |
584 |
11 |
53 |
1 |
227 |
585 |
7 |
83 |
4 |
228 |
589 |
2 |
294 |
1 |
229 |
590 |
587 |
1 |
3 |
230 |
593 |
5 |
118 |
3 |
231 |
596 |
8 |
74 |
4 |
232 |
600 |
599 |
1 |
1 |
233 |
601 |
199 |
3 |
4 |
234 |
605 |
3 |
201 |
2 |
235 |
607 |
4 |
151 |
3 |
236 |
610 |
4 |
152 |
2 |
237 |
612 |
7 |
87 |
3 |
238 |
615 |
2 |
307 |
1 |
239 |
616 |
10 |
61 |
6 |
240 |
622 |
3 |
207 |
1 |
241 |
623 |
4 |
155 |
3 |
242 |
626 |
9 |
69 |
5 |
243 |
631 |
4 |
157 |
3 |
244 |
634 |
631 |
1 |
3 |
245 |
637 |
317 |
2 |
3 |
246 |
640 |
11 |
58 |
2 |
247 |
642 |
11 |
58 |
4 |
248 |
646 |
4 |
161 |
2 |
249 |
648 |
7 |
92 |
4 |
250 |
652 |
3 |
217 |
1 |
251 |
653 |
6 |
108 |
5 |
252 |
658 |
4 |
164 |
2 |
253 |
660 |
7 |
94 |
2 |
254 |
662 |
659 |
1 |
3 |
255 |
665 |
9 |
73 |
8 |
256 |
673 |
2 |
336 |
1 |
257 |
674 |
11 |
61 |
3 |
258 |
677 |
3 |
225 |
2 |
259 |
679 |
5 |
135 |
4 |
260 |
683 |
4 |
170 |
3 |
261 |
686 |
3 |
228 |
2 |
262 |
688 |
3 |
229 |
1 |
263 |
689 |
6 |
114 |
5 |
264 |
694 |
4 |
173 |
2 |
265 |
696 |
7 |
99 |
3 |
266 |
699 |
17 |
41 |
2 |
267 |
701 |
349 |
2 |
3 |
268 |
704 |
19 |
37 |
1 |
269 |
705 |
7 |
100 |
5 |
270 |
710 |
709 |
1 |
1 |
271 |
711 |
353 |
2 |
5 |
272 |
716 |
23 |
31 |
3 |
273 |
719 |
3 |
239 |
2 |
274 |
721 |
359 |
2 |
3 |
275 |
724 |
5 |
144 |
4 |
276 |
728 |
727 |
1 |
1 |
277 |
729 |
727 |
1 |
2 |
278 |
731 |
4 |
182 |
3 |
279 |
734 |
9 |
81 |
5 |
280 |
739 |
2 |
369 |
1 |
281 |
740 |
11 |
67 |
3 |
282 |
743 |
2 |
371 |
1 |
283 |
744 |
13 |
57 |
3 |
284 |
747 |
4 |
186 |
3 |
285 |
750 |
9 |
83 |
3 |
286 |
753 |
751 |
1 |
2 |
287 |
755 |
11 |
68 |
7 |
288 |
762 |
4 |
190 |
2 |
289 |
764 |
761 |
1 |
3 |
290 |
767 |
3 |
255 |
2 |
291 |
769 |
383 |
2 |
3 |
292 |
772 |
3 |
257 |
1 |
293 |
773 |
769 |
1 |
4 |
294 |
777 |
5 |
155 |
2 |
295 |
779 |
5 |
155 |
4 |
296 |
783 |
19 |
41 |
4 |
297 |
787 |
5 |
157 |
2 |
298 |
789 |
787 |
1 |
2 |
299 |
791 |
6 |
131 |
5 |
300 |
796 |
397 |
2 |
2 |
301 |
798 |
4 |
199 |
2 |
302 |
800 |
3 |
266 |
2 |
303 |
802 |
797 |
1 |
5 |
304 |
807 |
5 |
161 |
2 |
305 |
809 |
5 |
161 |
4 |
306 |
813 |
2 |
406 |
1 |
307 |
814 |
5 |
162 |
4 |
308 |
818 |
3 |
272 |
2 |
309 |
820 |
19 |
43 |
3 |
310 |
823 |
2 |
411 |
1 |
311 |
824 |
7 |
117 |
5 |
312 |
829 |
2 |
414 |
1 |
313 |
830 |
3 |
276 |
2 |
314 |
832 |
6 |
138 |
4 |
315 |
836 |
7 |
119 |
3 |
316 |
839 |
2 |
419 |
1 |
317 |
840 |
9 |
93 |
3 |
318 |
843 |
29 |
29 |
2 |
319 |
845 |
419 |
2 |
7 |
320 |
852 |
5 |
170 |
2 |
321 |
854 |
23 |
37 |
3 |
322 |
857 |
3 |
285 |
2 |
323 |
859 |
853 |
1 |
6 |
324 |
865 |
431 |
2 |
3 |
325 |
868 |
433 |
2 |
2 |
326 |
870 |
4 |
217 |
2 |
327 |
872 |
7 |
124 |
4 |
328 |
876 |
19 |
46 |
2 |
329 |
878 |
19 |
46 |
4 |
330 |
882 |
881 |
1 |
1 |
331 |
883 |
4 |
220 |
3 |
332 |
886 |
883 |
1 |
3 |
333 |
889 |
887 |
1 |
2 |
334 |
891 |
7 |
127 |
2 |
335 |
893 |
887 |
1 |
6 |
336 |
899 |
2 |
449 |
1 |
337 |
900 |
13 |
69 |
3 |
338 |
903 |
17 |
53 |
2 |
339 |
905 |
17 |
53 |
4 |
340 |
909 |
907 |
1 |
2 |
341 |
911 |
907 |
1 |
4 |
342 |
915 |
4 |
228 |
3 |
343 |
918 |
457 |
2 |
4 |
344 |
922 |
919 |
1 |
3 |
345 |
925 |
13 |
71 |
2 |
346 |
927 |
2 |
463 |
1 |
347 |
928 |
6 |
154 |
4 |
348 |
932 |
7 |
133 |
1 |
349 |
933 |
929 |
1 |
4 |
350 |
937 |
311 |
3 |
4 |
351 |
941 |
11 |
85 |
6 |
352 |
947 |
2 |
473 |
1 |
353 |
948 |
5 |
189 |
3 |
354 |
951 |
13 |
73 |
2 |
355 |
953 |
5 |
190 |
3 |
356 |
956 |
953 |
1 |
3 |
357 |
959 |
3 |
319 |
2 |
358 |
961 |
2 |
480 |
1 |
359 |
962 |
239 |
4 |
6 |
360 |
968 |
3 |
322 |
2 |
361 |
970 |
4 |
242 |
2 |
362 |
972 |
17 |
57 |
3 |
363 |
975 |
971 |
1 |
4 |
364 |
979 |
977 |
1 |
2 |
365 |
981 |
6 |
163 |
3 |
366 |
984 |
983 |
1 |
1 |
367 |
985 |
7 |
140 |
5 |
368 |
990 |
7 |
141 |
3 |
369 |
993 |
5 |
198 |
3 |
370 |
996 |
7 |
142 |
2 |
371 |
998 |
7 |
142 |
4 |
372 |
1002 |
7 |
143 |
1 |
373 |
1003 |
4 |
250 |
3 |
374 |
1006 |
6 |
167 |
4 |
375 |
1010 |
503 |
2 |
4 |
376 |
1014 |
4 |
253 |
2 |
377 |
1016 |
337 |
3 |
5 |
378 |
1021 |
2 |
510 |
1 |
379 |
1022 |
509 |
2 |
4 |
380 |
1026 |
4 |
256 |
2 |
381 |
1028 |
3 |
342 |
2 |
382 |
1030 |
3 |
343 |
1 |
383 |
1031 |
11 |
93 |
8 |
384 |
1039 |
4 |
259 |
3 |
385 |
1042 |
4 |
260 |
2 |
386 |
1044 |
347 |
3 |
3 |
387 |
1047 |
4 |
261 |
3 |
388 |
1050 |
1049 |
1 |
1 |
389 |
1051 |
349 |
3 |
4 |
390 |
1055 |
3 |
351 |
2 |
391 |
1057 |
263 |
4 |
5 |
392 |
1062 |
4 |
265 |
2 |
393 |
1064 |
3 |
354 |
2 |
394 |
1066 |
4 |
266 |
2 |
395 |
1068 |
1063 |
1 |
5 |
396 |
1073 |
2 |
536 |
1 |
397 |
1074 |
4 |
268 |
2 |
398 |
1076 |
29 |
37 |
3 |
399 |
1079 |
29 |
37 |
6 |
400 |
1085 |
2 |
542 |
1 |
401 |
1086 |
19 |
57 |
3 |
402 |
1089 |
1087 |
1 |
2 |
403 |
1091 |
4 |
272 |
3 |
404 |
1094 |
9 |
121 |
5 |
405 |
1099 |
4 |
274 |
3 |
406 |
1102 |
4 |
275 |
2 |
407 |
1104 |
7 |
157 |
5 |
408 |
1109 |
2 |
554 |
1 |
409 |
1110 |
9 |
123 |
3 |
410 |
1113 |
11 |
101 |
2 |
411 |
1115 |
4 |
278 |
3 |
412 |
1118 |
3 |
372 |
2 |
413 |
1120 |
6 |
186 |
4 |
414 |
1124 |
3 |
374 |
2 |
415 |
1126 |
7 |
160 |
6 |
416 |
1132 |
5 |
226 |
2 |
417 |
1134 |
13 |
87 |
3 |
418 |
1137 |
2 |
568 |
1 |
419 |
1138 |
11 |
103 |
5 |
420 |
1143 |
2 |
571 |
1 |
421 |
1144 |
571 |
2 |
2 |
422 |
1146 |
9 |
127 |
3 |
423 |
1149 |
5 |
229 |
4 |
424 |
1153 |
5 |
230 |
3 |
425 |
1156 |
1153 |
1 |
3 |
426 |
1159 |
13 |
89 |
2 |
427 |
1161 |
6 |
193 |
3 |
428 |
1164 |
9 |
129 |
3 |
429 |
1167 |
4 |
291 |
3 |
430 |
1170 |
7 |
167 |
1 |
431 |
1171 |
12 |
97 |
7 |
432 |
1178 |
11 |
107 |
1 |
433 |
1179 |
4 |
294 |
3 |
434 |
1182 |
9 |
131 |
3 |
435 |
1185 |
6 |
197 |
3 |
436 |
1188 |
593 |
2 |
2 |
437 |
1190 |
1187 |
1 |
3 |
438 |
1193 |
2 |
596 |
1 |
439 |
1194 |
29 |
41 |
5 |
440 |
1199 |
5 |
239 |
4 |
441 |
1203 |
4 |
300 |
3 |
442 |
1206 |
5 |
241 |
1 |
443 |
1207 |
401 |
3 |
4 |
444 |
1211 |
3 |
403 |
2 |
445 |
1213 |
7 |
173 |
2 |
446 |
1215 |
1213 |
1 |
2 |
447 |
1217 |
10 |
121 |
7 |
448 |
1224 |
1223 |
1 |
1 |
449 |
1225 |
10 |
122 |
5 |
450 |
1230 |
4 |
307 |
2 |
451 |
1232 |
1229 |
1 |
3 |
452 |
1235 |
3 |
411 |
2 |
453 |
1237 |
5 |
247 |
2 |
454 |
1239 |
4 |
309 |
3 |
455 |
1242 |
1237 |
1 |
5 |
456 |
1247 |
2 |
623 |
1 |
457 |
1248 |
7 |
178 |
2 |
458 |
1250 |
7 |
178 |
4 |
459 |
1254 |
5 |
250 |
4 |
460 |
1258 |
3 |
419 |
1 |
461 |
1259 |
5 |
251 |
4 |
462 |
1263 |
2 |
631 |
1 |
463 |
1264 |
1259 |
1 |
5 |
464 |
1269 |
6 |
211 |
3 |
465 |
1272 |
5 |
254 |
2 |
466 |
1274 |
19 |
67 |
1 |
467 |
1275 |
10 |
127 |
5 |
468 |
1280 |
3 |
426 |
2 |
469 |
1282 |
1279 |
1 |
3 |
470 |
1285 |
1283 |
1 |
2 |
471 |
1287 |
1283 |
1 |
4 |
472 |
1291 |
1289 |
1 |
2 |
473 |
1293 |
5 |
258 |
3 |
474 |
1296 |
431 |
3 |
3 |
475 |
1299 |
5 |
259 |
4 |
476 |
1303 |
4 |
325 |
3 |
477 |
1306 |
4 |
326 |
2 |
478 |
1308 |
1307 |
1 |
1 |
479 |
1309 |
14 |
93 |
7 |
480 |
1316 |
3 |
438 |
2 |
481 |
1318 |
4 |
329 |
2 |
482 |
1320 |
439 |
3 |
3 |
483 |
1323 |
1319 |
1 |
4 |
484 |
1327 |
5 |
265 |
2 |
485 |
1329 |
7 |
189 |
6 |
486 |
1335 |
2 |
667 |
1 |
487 |
1336 |
6 |
222 |
4 |
488 |
1340 |
3 |
446 |
2 |
489 |
1342 |
6 |
223 |
4 |
490 |
1346 |
5 |
269 |
1 |
491 |
1347 |
17 |
79 |
4 |
492 |
1351 |
19 |
71 |
2 |
493 |
1353 |
5 |
270 |
3 |
494 |
1356 |
8 |
169 |
4 |
495 |
1360 |
271 |
5 |
5 |
496 |
1365 |
29 |
47 |
2 |
497 |
1367 |
4 |
341 |
3 |
498 |
1370 |
37 |
37 |
1 |
499 |
1371 |
683 |
2 |
5 |
500 |
1376 |
3 |
458 |
2 |