144 Jean-Marie De Koninck
2 208
the
11th
Keith number (see the number 197).
2 210
the smallest number n which can be written as the sum of the squares of two
prime numbers in three distinct ways: 2 210 =
192 +432
=
232 +412
=
292 +372
(see the number 338);
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = 10: here
2 210 = 2 · 5 · 13 · 17, 2 211 = 3 · 11 · 67 and 2 212 = 22 · 7 · 79; if nk stands for
the smallest number n such that ω(n) + ω(n + 1) + ω(n + 2) = k, we have the
following table:
k nk
4 4
5 10
6 20
7 68
8 154
k nk
9 644
10 2 210
11 6 578
12 35 308
13 92 378
k nk
14 310 154
15 1 042 404
16 5 617 870
17 35 515 634
18 184 055 430
2 281
the exponent of the
17th
Mersenne prime
22 281
1 (Robinson, 1952).
2 285
the fifth number which is not a palindrome, but whose square is a palindrome
(see the number 26).
2 295
the fifth positive solution x of the diophantine equation
x2
+ 999 =
y3
(see the
number 251).
2 303
the smallest solution of τ (n+1)−τ (n) = 21; the sequence of numbers satisfying
this equation begins as follows: 2 303, 24 649, 67 599, 85 849, 104 975, 132 495,
283 023, . . . (see the number 399).
2 309
the third prime number p of the form p =
r
i=1
pi 1: 2 309 = 2 · 3 · 5 · 7 · 11 1
(see the number 317).
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