300 Jean-Marie De Koninck
14 684 570
the number of possible arrangements of the integers 1,2,. . . ,11 with the restric-
tion that the integer j must not be in the j-th position for each j, 1 j 11
(see the number 265).
14 919 500
the smallest number which can be written as the sum of three fifth powers and
as the sum of four fifth powers: 14 919 500 =
35 +225 +255
=
15 +85 +145 +275;
the sequence of numbers satisfying this property begins as follows: 14 919 500,
31 325 350, 40 555 282, 48 960 099, 70 231 833, 83 419 269, 89 095 328, . . .
14 926 248
the smallest number which can be written as the sum of three distinct cubes
in nine distinct ways:
14 926 248 =
23
+
343
+
2463
=
123
+
1863
+
2043
=
153
+
333
+
2463
=
513
+
1143
+
2373
=
723
+
903
+
2403
=
753
+
1903
+
1973
=
903
+
1863
+
1983
=
993
+
1493
+
2203
=
1063
+
1503
+
2183
(see the number 1 009).
14 939 999
the eighth solution of σ2(n) = σ2(n + 2) (see the number 1 079).
15 474 787
the 1 000
000th
prime power, in fact here a prime number (see the number 419).
15 485 863
the 1 000 000th prime number (see the number 541).
15 760 091
the first member p of the second 8-tuple (p, p + 2, p + 6, p + 8, p + 12, p + 18, p +
20, p + 26) made up entirely of prime numbers: the first 8-tuple satisfying this
property is (11,13,17,19,23,29,31,37).
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