392 Jean-Marie De Koninck
2 658 455 991 569 831 744 654 692 615 953 842 176 (= 260(261 1))
the ninth even perfect number.
3 137 163 227 263 018 301 981 160 710 533 087 044
the fourth number which is not a fourth power but which can be written as the
sum of the fourth powers of some of its prime factors: here
3 137 163 227 263 018 301 981 160 710 533 087 044
=
22
·
32
· 7 · 11 · 191 · 283 · 7541 · 1330865843 · 2086223663996743
=
34
+
74
+
1914
+
13308658434;
the smallest number satisfying this property is 107 827 277 891 825 604.
115 132 219 018 763 992 565 095 597 973 971 522 401
the largest narcissistic number (D. Winter, 1985); see the number 88.
170 141 183 460 469 231 731 687 303 715 884 105 727
the 12th Mersenne prime, namely 2127 1.
340 282 366 920 938 463 463 374 607 431 768 211 457 (=
227
+ 1)
the eighth Fermat number: its factorization was obtained in 1974 by Morrison
and Brillhart:
227
+ 1 = 59 649 589 127 497 217 · 5 704 689 200 685 129 054 721.
437 489 361 912 143 559 513 287 483 711 091 603 378
the smallest known number n such that P (n)5|n and P (n + 1)5|(n + 1): here
437 489 361 912 143 559 513 287 483 711 091 603 378
= 2 ·
33
·
72
·
112
· 67 · 1151 · 1439 · 1609 · 2557 ·
49575,
437 489 361 912 143 559 513 287 483 711 091 603 379
= 43 · 61 · 107 · 269 · 421 · 617 · 653 · 2689 ·
66195;
the numbers 4402074374845013694517762402276831087215,
22748992615102631934745928628382078239867,
2954120615478394653060385065220308608058260,
8250351204235843413274102593592289950249874,
556676284977787252656476827071452300208916227 and
4556139057327711835147225814446398763593460517 also satisfy this property
(see the number 6 859).
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