194 Jean-Marie De Koninck

15 877

• the 18th (and largest known) prime number pk such that p1p2 . . . pk −1 is prime

(see the number 317).

16 111

• the prime number which appears the most often as the

17th

prime factor of an

integer (see the number 199).

16 363

• the third number which is equal to the sum of the fifth powers of its digits

added to the product of its digits (see the number 1 324).

16 447

• the 10

000th

square-free number (see the number 165).

16 513 (=

72

· 337)

• the second 6-hyperperfect number (see the number 301).

16 575

• the smallest number n such that β(n) ≤ β(n + 1) ≤ . . . ≤ β(n + 7); here

38 46 148 312 340 836 5530 8293 (see the number 714).

16 641

• the ninth powerful number which can be written as the sum of two co-prime

3-powerful numbers = 1: 16 641 = 2 000 + 14 641, that is

32

·

432

=

24

·

53

+

114

(see the number 841).

16 767

• the smallest number n such that n and n+1 are both divisible by a sixth power:

16 767 =

36

· 23, 16 768 =

27

· 131 (see the number 1 215).

16 787

• the smallest prime number equally distant, by a distance of 24, from the

preceding and following prime numbers: p1938 = 16 763, p1939 = 16 787 and

p1940 = 16 811.