Those Fascinating Numbers 179

8 638

• (probably) the largest number which cannot be written as the sum of two co-

prime numbers whose index of composition is ≥ 1.7 (see the number 933).

8 646

• the fifth number n such that 2n ≡ −2 (mod n) (see the number 946).

8 648

• the eighth dihedral perfect number (see the number 130).

8 672

• the smallest solution y of y2 =

(

x

0

)

+

(

x

1

)

+

(

x

2

)

+

(

x

3

)

, namely (x, y) = (767, 8672)

(see the number 767).

8 786

• the smallest solution of σ(n) = σ(n + 69): it is mentioned in R.K. Guy [101],

B13, that Mientka and Vogt could only find two solutions of this equation,

namely 8 786 and 24 885: but there are 35 more

107;

the sequence of num-

bers satisfying this property begins as follows: 8786, 24885, 205206, 274505,

414645, 554826, 622686, 724746, . . .

8 825

• the third composite number n (and the largest one known) such that σ(n +

2) − σ(n) = 2 (see the number 434).

8 855

• the eighth Lucas-Carmichael number (see the number 399).

8 911 (= 7 · 19 · 67)

• the seventh Carmichael number (see the number 561).

8 922

• the second solution of σ(n) = σ(n + 3) (see the number 382).