198 Jean-Marie De Koninck

18 620

• the ninth number which is not perfect or multi-perfect but whose harmonic

mean is an integer (see the number 140).

18 737

• the smallest number which can be written as the sum of two squares, as the

sum of two cubes and as the sum of two fourth powers and where each of the

numbers in question is distinct from the others: here 18 737 =

892

+

1042

=

173

+

243

=

84

+

114.

18 787

• the second component of the largest known pair of prime numbers (p, q) such

that

pq−1

≡ 1 (mod

q2)

and

qp−1

≡ 1 (mod

p2);

here (p, q) = (2903, 18787) (see the number 2 903).

18 885

• the

21rst

number n such that n ·

2n

− 1 is prime (see the number 115).

19 151

• the sixth self contained number (see the number 293).

19 279

• the number of Carmichael numbers 1013 (see the number 646).

19 333

• the smallest prime number p such that p + 40 is prime and such that each

number between p and p + 40 is composite (see the number 139).

19 469

• the 37th Lucas prime number (see the number 613).

19 521

• the third 2-hyperperfect number (see the number 21).