64 Jean-Marie De Koninck
the smallest number which is not the sum of five non zero distinct squares
(R.K. Guy [101], C20).
246
the third number n such that σ2(n) is a perfect square: we indeed have
σ2(246) =
2902
(see the number 42).
248
the smallest solution of σ(n) = σ(n + 37); the sequence of numbers satisfying
this equation begins as follows: 248, 302, 345, 518, 1142, 1298, 2108, 2174,
2505, 2678, 4604, . . .
249
the ninth number n such that n ·
2n
1 is prime (see the number 115).
250
the fourth solution of φ(n) = γ(n)2 (see the number 108).
251
the smallest number which can be written as the sum of three cubes in two
distinct ways: 251 =
13
+
53
+
53
=
23
+
33
+
63
(see the number 1 009);
the third positive solution x of the diophantine equation
x2
+ 999 =
y3
(R.
Steiner): the only positive solutions (x, y) of this diophantine equation are
(1, 10), (27, 12), (251, 40), (1 782, 147), (2 295, 174) and (3 370 501, 22 480).
255
the number of Carmichael numbers
108
(Poulet, 1938); see the number 646;
the seventh solution of φ(n) = φ(n + 1) (see the number 15).
256
the largest known power of 2 which can be written as a sum of distinct powers
of 3: here 256 =
28
=
35
+
32
+ 3 + 1 (see R.K. Guy [101], B33).
257
the fourth Fermat number: 257 =
223
+ 1; the first three are 3, 5 and 17;
the smallest number n such that φ8(n) = 2, where φ8(n) stands for the eighth
iteration of the φ function (see the number 137).
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