390 Jean-Marie De Koninck
113 423 713 055 421 844 361 000 443
the eighth voracious number (see the number 1 807).
244 197 000 982 499 715 087 866 346 (= 2 · 3 · 11 · 23 · 31 · 47 137 · 28 282 147)
the tenth Giuga number (see the number 30).
453 694 852 221 687 377 444 001 769
the smallest perfect square which can be written as the sum of 2, 3, 4, 5, 6 and
7 squares:
453 694 852 221 687 377 444 001 769
= 21 300 113 901
6132
= 21 300 113 901
6122
+ 6 526
8852
= 21 300 113 901
6122
+ 6 526
8842
+
36132
= 21 300 113 901
6122
+ 6 526
8842
+
36122
+
852
= 21 300 113 901
6122
+ 6 526
8842
+
36122
+
842
+
132
= 21 300 113 901
6122
+ 6 526
8842
+
36122
+
842
+
122
+
52
= 21 300 113 901
6122
+ 6 526
8842
+
36122
+
842
+
122
+
42
+
32.
618 970 019 642 690 137 449 562 111
the tenth Mersenne prime, namely
289
1.
6 658 606 584 104 736 522 240 000 000
the value of 1! · 2! · . . . · 10!.
27 134 923 845 424 074 797 548 044 288
the seventh (and possibly the largest) number which is equal to the product of
the factorials of its digits in base 5:
27 134 923 845 424 074 797 548 044 288
= [2, 4, 4, 2, 4, 3, 2, 2, 1, 0, 2, 3, 0, 2, 4, 4, 3, 1, 0, 3, 3, 4, 3, 3, 1, 2, 4, 4, 0, 3, 3,
4, 2, 4, 4, 4, 0, 4, 1, 2, 3]5 (see the number 144).
34 111 227 434 420 791 224 041 472 000 (=
227
·
35
·
53
· 7 · 11 ·
132
· 19 · 29 · 31 ·
43 · 61 · 113 · 127)
the second 6-perfect number: n is 6-perfect if σ(n) = 6n (see R.K. Guy [104],
B2).
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