Those Fascinating Numbers 169
5 851
the
30th
Lucas prime number (see the number 613).
5 879
the smallest number n such that the Liouville function λ0 takes successively,
starting with n, nine times in a row the value −1; if nk stands for the smallest
number n such that λ0(n + i) = −1 for i = 0, 1, 2, . . . , k 1, then we have the
following table:
k nk
1 1
2 2
3 11
4 17
5 27
6 27
7 170
8 279
9 428
10 5 879
k nk
11 5 879
12 13 871
13 13 871
14 13 871
15 171 707
16 171 707
17 1 004 646
18 1 004 646
19 1 633 357
20 5 460 156
k nk
21 11 902 755
22 21 627 159
23 21 627 159
24 38 821 328
25 41 983 357
26 179 376 463
27 179 376 463
28 179 376 463
29 179 376 463
30 179 376 463
(see the number 1 934 for the list of the smallest numbers nk such that λ0(nk +
i) = 1 for i = 0, 1, 2, . . . , k 1).
5 906
the smallest number which can be written as the sum of the fourth powers of
two rational numbers
(254
+
1494
= 5 906 ·
174),
but not the sum of the fourth
powers of two integers (A. Bremner & P. Morton [24]).
5 913
the value of 1! + 2! + . . . + 7!.
5 943
the fourth number n such that n, n + 1, n + 2 and n + 3 have the same number
of divisors, namely eight (see the number 242).
Previous Page Next Page