280 Jean-Marie De Koninck

1 747 591

• the third prime number p such that

13p−1

≡ 1 (mod

p2)

(see the number

863).

1 782 144 (= 27 · 32 · 7 · 13 · 17)

• the second solution of

σ(n)

n

=

15

4

(see the number 293 760).

1 799 938 (= 2 · 7 · 83 · 1549)

• the number n which allows the sum

m≤n

Ω(m)=4

1

m

to exceed 2 (see the number

10 305).

1 825 200

• the ninth powerful number n such that n + 1 is also powerful: here 1 825 200 =

24 · 33 · 52 · 132 and 1 825 201 = 72 · 1932 (see the number 288).

1 835 421

• the smallest number n which allows the sum

i≤n

1

i

to exceed 15 (see the num-

ber 83).

1 854 699

• the third number n for which ξ(n) is an integer (see the number 614 341).

1 940 450

• the ninth number n such that the binomial coeﬃcient

(

n

2

)

is a perfect square:

here

(1

940 450

2

)

=

13721052

(see the number 289).

1 950 625 (= 54 · 3121)

• the smallest 4-hyperperfect number: we say that a number n is 4-hyperperfect

if it can be written as n = 1 + 4

d|n

1dn

d (which is equivalent to the condition

4σ(n) = 5n + 3).