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).
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