154 Jean-Marie De Koninck

3 217

• the exponent of the

18th

Mersenne prime

23 217

− 1 (Riesel, 1957).

3 229

• the 11th prime number pk such that p1p2 . . . pk + 1 is prime (see the number

379).

3 237

• the second solution of σ2(n) = σ2(n + 6) (see the number 645).

3 250

• the

12th

number n such that f(n) f(m) for all numbers m n, where

f(n) :=

Σ∗

1

p

, where the star indicates that the sum runs through all the prime

numbers p n which do not divide

(

2n

n

)

: here f(3250) = 1.17924 . . . (see the

number 364).

3 255

• the

14th

solution of φ(n) = φ(n + 1) (see the number 15).

3 315

• the smallest solution of σ(n + 49) = σ(n) + 49.

3 363

• the eighth number n such that

n2

− 1 is powerful (see the number 485): here

3

3632

− 1 =

23

·

292

·

412.

3 371

• the fifth prime number q such that

∑

p≤q

p is a multiple of 100 (see the number

563).

3 375

• the fourth odd number n 1 such that γ(n)|σ(n) (see the number 135).