148 Jean-Marie De Koninck
2 520
the largest of the six highly composite numbers (the other five are 1, 2, 6, 12
and 60) which divide each of the larger highly composite numbers (S. Ratering
[167]);
the value of [1, 2, 3, . . . , 10], that is the least common multiple of the numbers
1 to 10;
the 18th highly composite number (see the number 180).
2 522
the smallest number n such that Ω(n) = Ω(n + 1) = . . . = Ω(n + 5): here this
common value is 3 (see the number 602).
2 525
the smallest number n which allows the sum
m≤n
1
σ(m)
to exceed 6 (see the
number 129).
2 548
the second number which is not a cube and which can be written as the sum
of the cubes of its prime factors: 2 548 =
22
·
72
· 13 =
23
+
73
+
133
(see the
number 378).
2 580
the 12th Keith number (see the number 197).
2 592
the only number of the form abca such that abca =
ab
·
ca;
indeed, here we have
2 592 =
25
·
92.
2 593
the first term of the smallest sequence of five consecutive prime numbers all
of the form 4n + 1; denoting by qk the first term of the first sequence of k
consecutive prime numbers all of the form 4n + 1, we have the following table:
k qk
1 5
2 13
3 89
4 389
5 2 593
k qk
6 11 593
7 11 593
8 11 593
9 11 593
10 373 649
k qk
11 766 261
12 3 358 169
13 12 204 889
14 12 270 077
15 12 270 077
k qk
16 12 270 077
17 297 387 757
18 297 779 117
19 297 779 117
20 1 113 443 017
(see the number 463 for the analogue problem with 4n + 3).
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