Those Fascinating Numbers 357
n the factors of Fn
0 3 (prime)
1 5 (prime)
2 17 (prime)
3 257 (prime)
4 65537 (prime)
5 641 · 6700417
6 274177 · 67280421310721
7 59649589127497217 · 57044689200685129054721
8 1238926361552897 · P62
9 2424833
·7455602825647884208337395736200454918783366342657 · P99
10 45592577 · 6487031809 · P40 · P252
11 319489 · 974849 · 167988556341760475137
·3560841906445833920513 · P564
12 114689 · 26017793 · 63766529 · 190274191361
·1256132134125569 · C1187
13 2710954639361 · 2663848877152141313
·3603109844542291969 · 319546020820551643220672513 · C2391
14 C4933
15 1214251009 · 2327042503868417
·168768817029516972383024127016961 · C9808
16 825753601 · 188981757975021318420037633 · C19694
17 31065037602817 · C39444
18 13631489 · 81274690703860512587777 · C78907
19 70525124609 · 646730219521 · C157804
20 C315653
21 4485296422913 · C631294
22 C1262612
23 167772161 · C2525215
24 C5050446
82 864 869 804
the
17th
Bell number (see the number 52).
83 763 206 255
the ninth Hamilton number (see the number 923).
86 409 838 577
the fifth number having two representations as the sum of two co-prime fourth
powers:
86 409 838 577 =
5424
+
1034
=
5144
+
3594
(see the number 635 318 657).
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