246 Jean-Marie De Koninck

188 355

• the second 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

188 355 = 3 · 5 · 29 · 433 =

52

+

292

+

4332

(see the number 870).

189 375

• the first of the smallest eight consecutive numbers at which the Ω(n) function

takes distinct values, namely here the values 6, 8, 1, 7, 3, 5, 2 and 4 (see the

number 726).

194 979

• the largest number which can be written as the sum of the fifth powers of its

digits: 194 979 =

15

+

95

+

45

+

95

+

75

+

95

(see the number 4 150).

195 556

• the only composite number n 109 such that σ(n + 10) = σ(n) + 10.

197 210

• the second number which can be written as the sum of the squares of two prime

numbers in 5 distinct ways (as well as 6 and 7): 197 210 =

312

+

4432

=

672

+

4392

=

1072

+

4312

=

1732

+

4092

=

1992

+

3972

=

2412

+

3732

=

3112

+

3172

(see the number 338).

199 584

• the second solution of

σ(n)

n

=

11

3

(see the number 35 640).

199 606

• the seventh number n such that 2n ≡ −2 (mod n) (see the number 946).

203 391

• the smallest number n such that n and n + 1 each have nine prime factors

(counting their multiplicity); indeed, 203 391 =

38

· 31 and 203 392 =

27

· 7 · 227

(see the number 135).