178 Jean-Marie De Koninck

8 208

• one of the four numbers which can be written as the sum of the fourth powers

of its digits: 8 208 = 84 + 24 + 04 + 84; the others are 1, 1 634 and 9 474.

8 241

• the number of Carmichael numbers

1012

(Jaeschke, 1990); see the number

646.

8 363

• the number of five digit prime numbers (see the number 21).

8 408

• the smallest number n such that π(n) = n/8 (see the number 330).

8 450

• the only solution n

1012

of σ(n) = 2n + 119.

8 467

• the

32nd

Lucas prime number (see the number 613).

8 521

• the eighth prime number of the form

(x4

+

y4)/2

(see the number 41): here

8 521 =

(74

+

114)/2.

8 539

• the smallest prime number q such that

∑

p≤q

p is divisible by 2 310 (= 2 · 3 · 5 ·

7 · 11): here this sum is equal to 4 218 060 (see the number 269).

8 549 (= 83 · 103)

• the third Canada perfect number: 82 + 52 + 42 + 92 = 83 + 103 (see the number

125).

8 575

• the second composite number n such that σ(n + 2) − σ(n) = 2 (see the number

434).