174 Jean-Marie De Koninck

6 880

• the largest four digit vampire number: here 6 880 = 86 · 80 (see the number

1 260).

6 912

• the seventh number n 1 such that φ(σ(n)) = n (see the number 128).

6 917

• the

21rst

number n such that n! − 1 is prime (see the number 166).

6 930

• the fifth solution w of the aligned houses problem (see the number 35).

6 977

• the seventh prime number q such that

∑

p≤q

p is a multiple of 100 (see the

number 563).

7 022

• the largest number n for which inequality pn ≤ n(log n+log log n−0.9385) does

not hold: here p7022 = 70919 7022(log 7022+log log 7022−0.9385) = 70918.6

(see G. Robin [175]).

7 055

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

7 140

• one of the five numbers (the others are 1, 10, 120 and 1 540) which are both

triangular and tetrahedral (see the number 10).

7 192

• the fifth bizarre number (see the number 70).

7 225

• the smallest perfect square m4

2

for which there exist numbers m1, m2, m3 such

that mi

2

− (mi −

1)2

= mi−1

2

for i = 2, 3, 4: here 7 225 =

852

=

842

+

132

=

842 + 122 + 52 = 842 + 122 + 42 + 32 (see the number 169).