56 Jean-Marie De Koninck
k p0(k) rank
1 2 1
2 3 2
3 5 and 7 3 and 4
4 13 6
5 23 9
6 47 15
k p0(k) rank
7 113 30
8 199 46
9 283 61
10 467 91
11 887 154
12 1 627 258
k p0(k) rank
13 2 083 409
14 4 297 590
15 6 397 834
16 10 343 1 270
17 16 111 1 876
18 24 251 2 699
200
the only solution n 1012 of σ(n) = 2n + 65 (see the number 196);
the only number n = 4 and smaller than 1010 such that n divides σ(n) + σ2(n).
201
the smallest composite number of the form k · 10k + 1; the sequence of num-
bers satisfying this property begins as follows: 201, 40 001, 500 001, 6 000 001,
70 000 001, 800 000 001, 100 000 000 001, 1 100 000 000 001, . . . (see the number
363).
203
the sixth Bell number (see the number 52).
204
the total number of squares one can reproduce on a check board, namely 1 of
dimension 8 × 8, 4 of dimension 7 × 7, 9 of dimension 6 × 6, 16 of dimension
5 × 5, 25 of dimension 4 × 4, 36 of dimension 3 × 3, 49 of dimension 2 × 2, and
finally 64 of dimension 1 × 1;
the second number (and possibly the largest !) whose square is the sum of
three consecutive cubes
(2042
=
233
+
243
+
253);
the smallest one is 6
(62
=
13
+
23
+
33);
the third solution w of the aligned houses problem (see the number 35).
205
the number of twin prime pairs 104 (see the number 1 224).
206
the second number n such that σ(n) = σ(n + 1) (see the number 14, as well as
the numbers 1 253 and 1 919).
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