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).
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