Those Fascinating Numbers 187

11 715

• the

19th

solution of φ(n) = φ(n + 1) (see the number 15).

11 872

• the number of Niven numbers ≤ 105 (see the number 213).

11 881 (=

1092)

• the smallest five digit perfect square which has only two distinct digits (see the

number 1 444);

• the second star number 1 which is also a perfect square (see the number

121).

11 907

• the seventh odd number n 1 such that γ(n)|σ(n) (see the number 135).

11 935

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

12 008

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

12 025

• the fifth number whose square can be written as the sum of three fourth powers:

12

0252

=

604

+

754

+

1004

(see the number 481).

12 101

• the smallest five digit prime number whose digits are consecutive (see the num-

ber 67).

12 167

• the fifth powerful number n such that n + 1 is also powerful (see the number

288): here 12 167 =

233

and 12 168 =

23

·

32

·

132.