170 Jean-Marie De Koninck

5 971

• the smallest composite Wilson number; setting S(n) :=

n

i=1

(i,n)=1

i, one can gen-

eralize Wilson’s Theorem by showing that S(n) ≡ −1 (mod n) if n = 2, 4, pb

or 2pb, where p is an odd prime number, and S(n) ≡ 1 (mod n) otherwise;

Wilson numbers are therefore defined as the numbers n for which S(n) ≡ ±1

(mod n2); the sequence of Wilson numbers begins as follows: 5, 13, 563, 5 971,

558 771, 1 964 215, 8 121 909, 12 326 713, 23 025 711, 26 921 605, 341 569 806,

399 292 158 (see T. Agoh, K. Dilcher & L. Skula [2]).

5 985

• the tenth odd abundant number (see the number 945).

5 993

• the largest known Stern number (see the number 137).

6 044

• the second number n such that σ(n), σ(n + 1), σ(n + 2) and σ(n + 3) have the

same prime factors, namely here 2, 3 and 7 (see the number 3 777).

6 048 (=

25

·

33

· 7)

• the second solution of

σ(n)

n

=

10

3

(see the number 1080).

6 079

• the largest known prime number which divides a Mersenne number (here

21013−

1) and is such that the prime number that follows, namely 6 089, is also a factor

of a Mersenne number (here

2761

− 1); see the number 1 433.

6 099

• the only four digit Sastry number (see the number 183); if nr stands for the

smallest r digit Sastry number, then n3 = 183, n4 = 6 099, n5 = 13 224,

n6 = 106 755, n7 = 2 066 115 and n8 = 22 145 328.

6 144

• the

12th

Granville number (see the number 126).