## Numerator of Σ(μ(n)/n) (n = 1 to 100)

(Complete : June 15, 2003)

Numerator of Σ(μ(n)/n) = Numerator of

1/1 + (-1/2) + (-1/3) + 0/4 + (-1/5) + 1/6 + ...

Factor (-1) is omitted.

```  n : N = factors

1 : 1 (1) = unit
2 : 1 (1) = unit
3 : 1 (1) = unit
5 : -1 (1) = unit
6 : 2 (1) = prime
7 : -1 (1) = unit

10 : 19 (2) = prime
11 : -1 (1) = unit
13 : -2323 (4) = 23 * 101
14 : -89 (2) = prime
15 : 304 (3) = 2^4 * 19
17 : 163 (3) = prime
19 : -81988 (5) = 2^2 * 103 * 199

21 : -15019 (5) = 23 * 653
22 : 410857 (6) = prime
23 : -249979 (6) = 457 * 547
26 : 4165258 (7) = 2 * 743 * 2803
29 : 9246047 (7) = prime

30 : -65721449 (8) = 2411 * 27259
31 : -4193929329 (10) = 3 * 2213 * 631711
33 : -6504197377 (10) = 257 * 25308161
34 : -302679716 (9) = 2^2 * 75669929
35 : 2562470143 (10) = 139 * 18435037
37 : -5468849774 (10) = 2 * 773 * 1301 * 2719
38 : 184344882947 (12) = prime
39 : 124873406579 (12) = 97 * 191 * 6740077

41 : 2646230291469 (13) = 3 * 3 * 16007 * 18368563
42 : 347318490451 (12) = prime
43 : -137190436674212 (15) = 2^2 * 171937 * 199477769
46 : 10026981687881 (14) = prime
47 : -12611493192339623 (17) = 238361 * 52909214143

51 : -184943596214571 (15) = 3 * 13457 * 4581100201
53 : -214765271462202733 (18) = 331 * 3083 * 210456593621
55 : -17255220085293371 (17) = prime
57 : 519973962150962777 (18) = 2677 * 194237565241301
58 : 540928002430567981 (18) = 2342407 * 230928272683
59 : 15620172904808488514 (20) = 2 * 73 * 65479 * 1633920579871

61 : -8549627883788520181 (19) = 79 * 2351 * 46032810620789
62 : 1874648830674470878723 (22) = 7460131681 * 251288973283
65 : 3679085466973039663081 (22) = 11651568301 * 315758820781
66 : 316998129951549613081 (21) = 97 * 461 * 643 * 2347 * 4697426333
67 : 1690811146852662245882 (22) = 2 * 1151 * 250441949 * 2932801759
69 : 62016792506357023374451 (23) = 167 * 371358038960221696853

70 : 336338530534578047569 (21) = 389 * 864623471811254621
71 : -200643437220052588790575 (24) = 5^2 * 307 * 32429 * 9018413 * 89388757
73 : -30588137492112380723638129 (26) = 139 * 220058543108722163479411
74 : -7431196043498463691814948 (25) = 2^2 * 1783 * 1041951211931921437439
77 : 877316785444551755504875 (24) = 5^3 * 2857 * 4021 * 610944996203987
78 : -34226814962907926308826941 (26) = prime
79 : -5419230422019661121772083237 (28) = 10529 * 225371 * 2283770505978934943

82 : -1401629533229069216211617003 (28) = 397 * 9463 * 373090244153637011873
83 : -223590076836035175208867029720 (30) = 2^3 * 3 * 5 * 20903 * 89137953418183663911427
85 : -594294471063948716523503740771 (30) = 157 * 59053 * 1052656421 * 60893849298431
86 : -153455160386518164226759349787 (30) = 3 * 6403002929 * 7988707907217543001
87 : 2609341595728673683821147444809 (31) = 181 * 661 * 21809760832228698220686449
89 : -34833113669423893495541895404789 (32) = 197 * 2607335771 * 67815521825785005347

91 : 226361852224483257830288188126621 (33) = 227 * 60077 * 71171 * 476713 * 489225494353313
93 : 160646574025887074368700140133097 (33) = 3 * 389149 * 2284963 * 60221992805425818677
94 : 122466446403627137841531874324276 (33) = 2^2 * 1274485613 * 24022720451773969503713
95 : 164165993590198279544427554326659 (33) = 3 * 283 * 24527 * 170575243 * 46218418375175831
97 : 11962644395524974654034383169459538 (35) = 2 * 52859 * 672091355671 * 168364275146737421
```

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima