Those Fascinating Numbers 349

7 826 354 460 (= 22 · 311 · 5 · 472)

• the number amongst those

1011,

whose index of composition is the nearest

to π: here λ(7826354460) ≈ 3.14159213 (see the number 93 112 129 088 for the

analogue situation with the Euler number e, as well as the method used to

obtain this type of result).

8 303 765 625

• the second number n 1 whose sum of digits is equal to

6

√

n (see the number

34 012 224).

8 583 644 160 (=

210

·

32

· 5 · 7 · 13 · 23 · 89)

• the third solution of

σ(n)

n

=

9

2

(see the number 8 910 720).

8 589 869 056 (= 216(217 − 1))

• the sixth perfect number.

8 589 934 590 (= 2 · 3 · 5 · 17 · 257 · 65537)

• the sixth number n such that σ(φ(n)) = n/2: the first five are 2, 6, 30, 510 and

131 070.

8 657 437 697

• the third number having two representations as the sum of two fourth powers:

8 657 437 697 =

1934

+

2924

=

2564

+

2574

(see the number 635 318 657).

9 000 000 001

• the third prime number of the form k · 10k +1 (see the numbers 3 001 and 201).

9 480 294 330 (= 2 · 3 · 5 · 13 · 23 · 47 · 113 · 199)

• the

13th

ideal number (see the number 390).

9 876 543 210

• the only ten digit self replicating number (see the number 954).