162 Jean-Marie De Koninck

4 481

• the sixth prime number of the form

(x4

+

y4)/2:

here 4 481 =

(74

+

94)/2

(see

the number 41).

4 503

• the third number n such that n, n + 1, n + 2 and n + 3 have the same number

of divisors, in this case eight (see the number 242).

4 547

• the

12th

prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

4 550

• the smallest number n which allows the sum

i≤n

1

i

to exceed 9 (see the number

83).

4 567

• the only four digit prime number, whose digits are consecutive (see the number

67).

4 583

• the

15th

prime number pk such that p1p2 . . . pk − 1 is prime (see the number

317).

4 649

• the largest prime factor of 1234567654321.

4 650

• the smallest number n such that

∑

m≤n

τ (m) is a multiple of 10 000 (here the

sum is equal to 40 000).

4 680 (=

23

·

32

· 5 · 13)

• the second solution of

σ(n)

n

=

7

2

(see the number 4 320).