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.
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