250 Jean-Marie De Koninck

228 727

• the third composite number n such that

2n−2

≡ 1 (mod n); see the number

20 737.

229 999

• the largest number n such that f5(n) n, where f5(n) = f([d1, d2, . . . , dr]) =

d1

5

+ d2

5

+ . . . + dr

5,

where d1, d2, . . . , dr stand for the digits of n.

230 387

• the smallest number n such that π(n)

n

log n

+

n

log2

n

+

2n

log3

n

+

6n

log4

n

, this

last expression representing the first four terms of the asymptotic expansion of

Li(n): here we have π(230387) = 20474 while

n

log n

+

n

log2

n

+

2n

log3

n

+

6n

log4

n

n=230387

≈ 20473.9 (see the number 73).

230 578

• the second even number n such that σI (n) = σI (n+2) (see the number 54 178).

230 769

• the sixth number which quadruples when its last digit is moved in first position

(see the number 102 564).

234 256 (=

224)

• the second number n 1 whose sum of digits is equal to

4

√

n (see the number

2 401).

234 613

• the smallest number n such that τ (n) ≤ τ (n + 1) ≤ . . . ≤ τ (n + 8): here

4 ≤ 4 8 ≤ 8 ≤ 8 ≤ 8 12 ≤ 12 ≤ 12 (see the number 241).

235 224

• the sixth powerful number n such that n + 1 is also powerful (see the number

288): here 235 224 = 23 · 35 · 112 and 235 225 = 52 · 972.

241 603

• the first term of the smallest sequence of 11 consecutive prime numbers all of

the form 4n + 3 (as well as 12 or 13 consecutive prime numbers all of the form

4n + 3); see the number 463.