192 Jean-Marie De Koninck

14 722

• the smallest number which can be written as the sum of two distinct fourth

powers and as the sum of four distinct fourth powers: 14 722 =

34

+

114

=

14 + 54 + 84 + 104; the sequence of numbers satisfying this property begins as

follows: 14722, 32657, 49297, 132722, 198577, 235552, 300577, 393026, . . .

14 833

• the number of possible arrangements of the integers 1,2,. . . ,8 with the restric-

tion that the integer j must not be in the

jth

position for each j, 1 ≤ j ≤ 8

(see the number 265).

14 841

• the tenth solution of σ(n) = σ(n + 1) (see the number 206).

14 884

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

4-powerful numbers: 14 884 = 243 + 14 641, that is

22

·

612

=

35

+

114

(see the

number 12 769);

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

3-powerful numbers = 1: 14 884 = 243 + 14 641, that is

22

·

612

=

35

+

114

(see

the number 841).

15 015 (= 3 · 5 · 7 · 11 · 13)

• the smallest odd square-free abundant number.

15 120

• the 22nd highly composite number (see the number 180).

15 121

• the smallest prime number p such that Ω(p +1) = 2, Ω(p +2) = 3, Ω(p +3) = 4

and Ω(p + 4) = 5 (see the number 61).

15 193

• the smallest prime factor of the Mersenne number

2211

− 1, whose complete

factorization is given by

2211

− 1 = 15193 · 60272956433838849161

·3593875704495823757388199894268773153439.