Those Fascinating Numbers 251

246 683

• the number of Carmichael numbers

1016

(see the number 646).

247 141

• the smallest prime number equally distant, by a distance of 42, from the pre-

ceding and following prime numbers: p21805 = 247 099, p21806 = 247 141 and

p21807 = 247 183.

248 397

• the smallest number n which allows the sum

i≤n

1

i

to exceed 13 (see the number

83).

248 832 (=

125)

• the smallest fifth power which can be written as the sum of six fifth powers:

248 832 =

125

=

45

+

55

+

65

+

75

+

95

+

115

(Martin, 1887).

253 472 (= 2 · 5 ·

892)

• the 1 000th powerful number (see the number 3 136).

254 540

• the smallest number n such that ω(n) = ω(n + 1) = 5; in fact, 254 540 =

22

· 5 · 11 · 13 · 89 and 254 541 = 3 · 7 · 17 · 23 · 31 (see the number 230).

255 803

• the smallest prime number equally distant, by a distance of 36, from the pre-

ceding and following prime numbers: p22506 = 255 767, p22507 = 255 803 and

p22508 = 255 839.

261 120

• the sixth number n divisible by a square 1 and such that γ(n + 1) − γ(n) = 1

(see the number 48).

262 419

• the tenth number n 1 such that n · 2n + 1 is prime (see the number 141).