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).