300 Jean-Marie De Koninck

14 684 570

• the number of possible arrangements of the integers 1,2,. . . ,11 with the restric-

tion that the integer j must not be in the j-th position for each j, 1 ≤ j ≤ 11

(see the number 265).

14 919 500

• the smallest number which can be written as the sum of three fifth powers and

as the sum of four fifth powers: 14 919 500 =

35 +225 +255

=

15 +85 +145 +275;

the sequence of numbers satisfying this property begins as follows: 14 919 500,

31 325 350, 40 555 282, 48 960 099, 70 231 833, 83 419 269, 89 095 328, . . .

14 926 248

• the smallest number which can be written as the sum of three distinct cubes

in nine distinct ways:

14 926 248 =

23

+

343

+

2463

=

123

+

1863

+

2043

=

153

+

333

+

2463

=

513

+

1143

+

2373

=

723

+

903

+

2403

=

753

+

1903

+

1973

=

903

+

1863

+

1983

=

993

+

1493

+

2203

=

1063

+

1503

+

2183

(see the number 1 009).

14 939 999

• the eighth solution of σ2(n) = σ2(n + 2) (see the number 1 079).

15 474 787

• the 1 000

000th

prime power, in fact here a prime number (see the number 419).

15 485 863

• the 1 000 000th prime number (see the number 541).

15 760 091

• the first member p of the second 8-tuple (p, p + 2, p + 6, p + 8, p + 12, p + 18, p +

20, p + 26) made up entirely of prime numbers: the first 8-tuple satisfying this

property is (11,13,17,19,23,29,31,37).