Those Fascinating Numbers 191

13 803

• the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) + ω(n + 3) = 14:

here 13 803 = 3 · 43 · 107, 13 804 = 22 · 7 · 17 · 29, 13 805 = 5 · 11 · 251 and

13 806 = 2 · 32 · 13 · 59 (see the number 987).

13 860

• the sixth solution y of the Fermat-Pell equation x2 − 2y2 = 1: here (x, y) =

(19601, 13860) (see the number 99).

13 896

• the smallest number which can be written as the sum of three distinct cubes

in four distinct ways:

13 896 =

13

+

123

+

233

=

23

+

43

+

243

=

43

+

183

+

203

=

93

+

103

+

233

(see the number 1 009).

13 963

• the

35th

Lucas prime number (see the number 613).

14 007

• the smallest number n such that the decimal expansion of

2n

contains eight

consecutive zeros (see the number 53).

14 322

• the smallest integer n such that ω(n), ω(n + 1), ω(n + 2), ω(n + 3), ω(n + 4)

are all distinct, namely in this case with the values 5, 1, 2, 3 and 4; here,

14 322 = 2 · 3 · 7 · 11 · 31, 14 323 = 14 323, 14 324 =

22

· 3581, 14 325 = 3 ·

52

· 191

and 14 326 = 2 · 13 · 19 · 29 (see the number 417).

14 336

• the

13th

Granville number (see the number 126).

14 449

• the 36th Lucas prime number (see the number 613).