Those Fascinating Numbers 239
130 304
the sixth solution of σ(n) = 2n + 2 (see the number 464).
131 052
the smallest Niven number n 6 such that n + 1, n + 2, n + 3 and n + 4 are
also Niven numbers (see the number 110).
131 070
the fifth number n such that σ(φ(n)) = n/2: the first four are 2, 6, 30 and 510;
the sixth one is 8 589 934 590.
131 071
the sixth Mersenne prime: 131 071 = 217 1: the following table provides the
list of all Mersenne primes 2p 1 known as of May 2009:
Rank p 2p 1
1 2 3
2 3 7
3 5 31
4 7 127
5 13 8 191
6 17 13 1071
7 19 524 287
8 31 2 147 483 647
9 61 261 1
10 89 289 1
11 107
2107
1
12 127
2127
1
13 521
2521
1
14 607
2607
1
15 1 279
21 279
1
16 2 203
22 203
1
17 2 281
22 281
1
18 3 217
23 217
1
19 4 253
24 253
1
20 4 423
24 423
1
21 9 689
29 689
1
22 9 941
29 941
1
23 11 213
211 213
1
Rank p 2p 1
24 19 937
219 937
1
25 21 701 221 701 1
26 23 209 223 209 1
27 44 497 244 497 1
28 86 243 286 243 1
29 110 503 2110 503 1
30 132 049 2132 049 1
31 216 091 2216 091 1
32 756 839 2756 839 1
33 859 433 2859 433 1
34 1 257 787
21 257 787
1
35 1 398 269
21 398 269
1
36 2 976 220
22 976 220
1
37 3 021 377
23 021 377
1
38 6 972 593
26 972 593
1
39 13 466 917
213 466 917
1
40 20 996 011
220 996 011
1
41 24 036 583
224 036 583
1
42 25 964 951
225 964 951
1
43 30 402 457
230 402 457
1
44 32 582 657
232 582 657
1
45 37 156 667
237 156 667
1
46 43 112 609
243 112 609
1
131 625
the sixth of the existing eight primitive non deficient numbers (see the number
945).
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