176 Jean-Marie De Koninck

7 560

• the smallest highly composite number which is not superabundant (see the

number 110 880): it is the 20th highly composite number (see the number 180).

7 641

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

7 647

• the 16th Keith number (see the number 197).

7 696

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

powers: 7 6962 = 484 + 604 + 804 (see the number 481).

7 741

• the 31rst Lucas prime number (see the number 613).

7 744 (= 882)

• the largest four digit perfect square which has only two distinct digits (see the

number 1 444).

7 755

• the

17th

number n such that n ·

2n

− 1 is prime (see the number 115).

7 776

• the fourth number n 2 such that

σ(n) + φ(n)

γ(n)2

is an integer (see the number

588).

7 785

• the fourth number n such that

∑

p≤pn

p is a perfect square: here

∑

p≤p7785

p =

17

0982

(see the number 2 474).

7 909

• the

17th

Keith number (see the number 197).