290 Jean-Marie De Koninck

5 096 876

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

5 099 011 (= 19 · 167 · 1607)

• the number n which allows the sum

m≤n

ω(m)=3

1

m

to exceed 4 (see the number

1 953).

5 134 240

• the largest number which is not the sum of distinct fourth powers (see Journal

of Recreational Mathematics 20 (1988), p. 316).

5 153 633

• the smallest number which can be written as the sum of two fifth powers and

as the sum of five fifth powers: 5 153 633 =

15

+

225

=

45

+

55

+

75

+

165

+

215.

5 195 977

• the smallest prime number q which allows the sum

p≤q

1

p

to exceed 3 (see the

number 277).

5 296 623 (= 3 · 1765541)

• the number n which allows the sum

m≤n

Ω(m)=2

1

m

to exceed 4 (see the number 871).

5 315 625 (= 35 · 55 · 7)

• the smallest number n having at least two distinct prime factors and such that

β(n)3 = B1(n): here (3 + 5 + 7)3 = 35 + 55 + 7 = 3375 (see also the number

5 120).

5 617 820

• the smallest number n such that ω(n)+ω(n+1)+ω(n+2) = 16: here 5 617 820 =

22

·5·13·17·31·41, 5 617 821 = 3·11·37·43·107 and 5 617 822 = 2·7·29·101·137

(see the number 2 210).