Those Fascinating Numbers 203

22 480

• the sixth and largest solution y of the diophantine equation

x2

+ 999 =

y3

(see

the number 251).

22 624

• the smallest number n such that each of the numbers n+i, 0 ≤ i ≤ 3, is divisible

by a cube 1: 22 624 = 25 · 7 · 101, 22 625 = 53 · 181, 22 626 = 2 · 33 · 419,

22 627 =

113

· 17 (see the number 242).

22 736

• the largest number n such that the corresponding triangular number Tn =

n(n+1)

2

is the product of three consecutive numbers: here

22 736 · 22 737

2

= 636 · 637 · 638

(see the number 608).

22 865

• the seventh number which is not a palindrome, but whose square is a palindrome

(see the number 26).

22 932

• the second number n such that

σ(n)

n

=

k

6

for some k satisfying (k, 6) = 1, here

with k = 19; the only solutions n

109

of this equation are 18, 22 932 and

14 520 576.

22 971

• the

22nd

number n such that n ·

2n

− 1 is prime (see the number 115).

23 005

• the 23rd number n such that n · 2n − 1 is prime (see the number 115).

23 209

• the exponent of the

26th

Mersenne prime

223 209

− 1 (Noll, 1979).