a（5）=7，因为1+2*7+3*7^2=162=2*3^4有5个素数除数，用重数计算。
设m=1+2*k+3*k^2。由于没有这样的数字m可以被2^2、5或7整除，因此具有给定数量的素数因子的最小数字m在其素数因子中往往有大量的3：
.
n k=a（n）m=1+2*k+3*k^2
-- ------------ -----------------------------------------------------
0 0 1
1 2 17（素数）
2 1 6 = 2 * 3
3 13 534 = 2 * 3 * 89
4 19 1122 = 2 * 3 * 11 * 17
5 7 162 = 2 * 3^4
6 61 11286 = 2 * 3^3 * 11 * 19
7 331 329346 = 2 * 3^4 * 19 * 107
8 169 86022 = 2 * 3^6 * 59
9 1141 3907926 = 2 * 3^5 * 11 * 17 * 43
10 6487 126256482 = 2 * 3^5 * 11^2 * 19 * 113
11 898 2421009 = 3^10 * 41
12 20581 1270773846 = 2 * 3^9 * 19 * 1699
13 315826 299238818481 = 3^9 * 19 * 73 * ...
14 59947 10781048322 = 2 * 3^10 * 11 * 43 * 193
15 296143 263102621634 = 2 * 3^12 * 17 * 14561
16 1890466 10721588872401 = 3^12 * 11 * 19 * ...
17 6141994 113172283172097 = 3^16 * 2629057
18 1359025 5540849569926 = 2 * 3^14 * 11^2 * 4787
19 49188715 7258589148431106 = 2 * 3^17 * 28103531
20 20490901 1259631112357206 = 2 * 3^15 * 17 * 73 * ...
21 264422320 209757490471391841 = 3^16 * 11 * 17 * ...
22 178328878 95403566542874409 = 3^19 * 19 * 83 * ...
23 1340590345 5391547422002837766 = 2 * 3^19 * 11^2 * ...
24 9476420614 269407642979285252217 = 3^22 * 2617 * ...
25 5989636213 107627225904222216534 = 2 * 3^20 * 19 * 97 * ...
26 72238539832 15655219911322828844337 = 3^22 * 11 * 19 * ...
27 103619599441 32211064165147101736326 = 2 * 3^22 * 11 * 43 * ...
28 668478672403 1340591206374369138728034 = 2 * 3^22 * 19 * 331 * ...
29 794002910839 1891321867264002956873442 = 2 * 3^23 * 11 * 73 * ...
30 417430195531 522743904423981537506946 = 2 * 3^25 * 11 * 17 * ...
.
因此，a（n）的三元表示的最后一位数字往往属于一种模式：
.
基数3中的na（n）a（n）
-- ------------ ---------------------------
0 0 0_3
1 2 2_3
2 1 1_3
3 13 111_3
4 19 201_3
5 7 21_3
6 61 2021_3
7 331 110021_3
8 169 20021_3
9 1141 1120021_3
10 6487 22220021_3
11 898 1020021_3
12 20581 1001020021_3
13 315826 121001020021_3
14 59947 10001020021_3
15 296143 120001020021_3
16 1890466 10120001020021_3
17 6141994 102120001020021_3
18 1359025 2120001020021_3
19 49188715 10102120001020021_3
20 20490901 1102120001020021_3
21 264422320 200102120001020021_3
22 178328878 110102120001020021_3
23 1340590345 10110102120001020021_3
24 9476420614 220110102120001020021_3
25 5989636213 120110102120001020021_3
26 72238539832 20220110102120001020021_3
27 103619599441 100220110102120001020021_3
28 668478672403 2100220110102120001020021_3
29 794002910839 2210220110102120001020021_3
30 417430195531 1110220110102120001020021_3
（结束）
