Those Fascinating Numbers 295

9 694 845

• the

15th

Catalan number (see the number 14).

9 745 728

• the

13th

number n such that φ(n) + σ(n) = 3n (see the number 312).

9 800 817

• the third number n 1 which can be written as the sum of the seventh powers

of its digits (see the number 1 741 725).

9 841 094

• the second number n such that P

(n)2|n,

P (n +

1)2|n

+ 1 and P (n +

2)2|n

+ 2:

here 9 841 094 =

2·67·2712,

9 841 095 =

34 ·5·11·472

and 9 841 096 =

23 ·17·2692

(see the number 1 294 298).

9 876 413

• the largest prime number made up of exactly seven distinct digits (see the

number 9 871).

9 926 315

• the fourth number n 1 which can be written as the sum of the seventh powers

of its digits (see the number 1 741 725).

9 980 583

• the fifth number n such that

n2

+ 2 is powerful: here

9 980

5832

+ 2 = 99612037019891 =

113

·

2735692

(see the number 265).

9 999 991

• the largest seven digit prime number.

10 000 019

• the smallest eight digit prime number.