Those Fascinating Numbers 327

275 305 224

• the number of 5 × 5 magic squares, excluding rotations and reflections (see the

number 880).

275 890 944

• the sixth solution of

σ(n)

n

=

10

3

(see the number 1 080).

282 977 280 (=

210

·

33

· 5 · 23 · 89)

• the fourth solution of

σ(n)

n

=

15

4

(see the number 293 760).

283 417 216

• the 20th dihedral perfect number (see the number 130).

292 965 218

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

powers in five and in six distinct ways:

292 965 218 =

24

+

1094

+

1114

=

214

+

984

+

1194

=

274

+

944

+

1214

=

344

+

894

+

1234

=

494

+

774

+

1264

=

614

+

664

+

1274

(see the number 6 578).

297 387 757

• the first term of the smallest sequence of 17 consecutive prime numbers all of

the form 4n + 1 (see the number 2 593).

297 779 117

• the first term of the smallest sequence of 18 consecutive prime numbers all of

the form 4n + 1 (see the number 2 593).

298 995 972

• the third number which is not the square of a prime number, but which can be

written as the sum of the squares of some of its prime factors: here 298 995 972 =

22

· 3 · 11 · 131 · 17291 =

32

+

112

+

1312

+

172912

(see the number 870).