168 Jean-Marie De Koninck

5 733

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

5 775

• the smallest abundant number n such that n +1 is also abundant; the sequence

of numbers satisfying this property begins as follows: 5775, 5984, 7424, 11024,

21735, 21944, 26144, 27404, 39375, 43064, . . .

5 776

• the sixth powerful number which can be written as the sum of two co-prime

3-powerful numbers = 1: 5 776 = 2 401 + 3 375, that is

24

·

192

=

74

+

33

·

53

(see the number 841).

5 777

• the smallest composite Stern number (see the number 137).

5 778

• the only triangular number 3 which is also a Lucas number (L. Ming [137]).

5 795

• the third number n 1 such that n ·

2n

+ 1 is prime (see the number 141).

5 828

• the smallest number n such that P (n + i) ≤

√

n + i for i = 0, 1, 2, 3, 4; the

largest prime factors of these five numbers are respectively 47, 67, 53, 17 and

3, all smaller than

√

5828 ≈ 76 (see the number 1 518).

5 830

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

5 832 (=183)

• the third number n whose sum of digits is equal to

3

√

n (see the number 512);

• the smallest cube which can be written as the sum of three cubes in two distinct

ways: 5 832 =

183

=

23 +123 +163

=

93 +123 +153;

if nk stands for the smallest

cube which can be written as the sum of three cubes in k distinct ways, we have

n1 = 216 =

63,

n2 = 5 832 =

183,

n3 = 157 464 =

543,

n4 = 658 503 =

873,

n5 = 1 259 712 =

1083,

n6 = n7 = 5 268 024 =

1743,

n8 = n9 = n10 =

34 012 224 =

3243,

n11 = n12 = n13 = 119 095 488 =

4923,

n14 = n15 =

952 763 904 = 9843.