346 Jean-Marie De Koninck

4 294 967 295

• the largest known number n such that σ(φ(n)) = γ(n); the known numbers

satisfying this equation are

3 = 3,

15 = 3 · 5,

255 = 3 · 5 · 17,

2 418 = 2 · 3 · 13 · 31,

65 535 = 3 · 5 · 17 · 257,

110 771 178 = 2 · 3 · 7 · 19 · 127 · 1093,

4 294 967 295 = 3 · 5 · 17 · 257 · 65537

(see also the number 744).

4 294 967 297 (=

225

+ 1 = 641 · 6 700 417)

• the sixth Fermat number, and the smallest composite one.

4 428 914 688 (= 213 · 32 · 11 · 43 · 127)

• the fourth solution of

σ(n)

n

=

13

4

(see the number 360).

4 473 671 462

• the fourth number which can be written as the sum of the cubes of its prime

factors:

4 473 671 462 = 2 · 13 · 179 · 593 · 1621 =

23

+

133

+

1793

+

5933

+

16213

(see the number 378).

4 679 307 774

• the smallest number which is equal to the sum of the tenth powers of its digits.

4 700 063 497 (= 19 · 47 · 5 263 229)

• the smallest solution of

2n

≡ 3 (mod n) (see R.K. Guy [101], F10).

4 758 958 741

• the smallest prime number p such that p + 300 is prime and such that each

number between p and p + 300 is composite (see the number 396 733).