296 Jean-Marie De Koninck

10 000 095

• the smallest Niven number n 5 such that n+1, n+2, n+3, n+4 and n+5 are

also Niven numbers (see the number 110); it is also the smallest Niven number

n 4 such that n +1, n +2, n +3, n +4, n +5 and n +6 are also Niven numbers.

10 234 589

• the smallest prime number made up of eight distinct digits (see the number

1 039).

10 708 555 (= 5 · 11 · 13 · 17 · 881)

• the 10 000 000th composite number (see the number 133).

10 729 219

• the fifth prime number q such that

∑

p≤q

p is a perfect square: here

p≤10729219

p = 3672424151449 = (463 ·

4139)2

(see the number 22 073).

10 869 375

• the fourth number n such that β(n)|β(n+1) and β(n+1)|β(n+2), here 67|1742

and 1742|15678 (see the number 225 504).

11 242 770

• the smallest number n such that φ(n + 1) = 5φ(n); the sequence of numbers

satisfying this property begins as follows: 11 242 770, 18 673 201, 77 805 000,

117 138 840, 122 649 450, . . . (see the number 1 260).

11 243 154

• the smallest number n such that ω(n) = ω(n + 1) = 6: here 11 243 154 =

2 · 3 · 13 · 17 · 61 · 139 and 11 243 155 = 5 · 7 · 11 · 19 · 29 · 53 (see the number 230).

11 309 768

• the tenth powerful number n such that n +1 is also powerful: here 11 309 768 =

23

·

292

·

412

and 11 309 769 =

32

·

192

·

592

(see the number 288).